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CORRELATION AND CONSERVATION 



Gravitation and Heat, 



SOME OF THE EFFECTS OF THESE FORCES 
ON THE SOLAR SYSTEM. 



J 



By ETHAN Sr CHAPIN. 



SPRINGFIELD, MASS. : 

LEWIS J. POWERS & BROTHER. 

1867. 



Entered according to Act of Congress, in the year 1867, by 
ETHAN S. CHAPIN, 
In the Clerk's Office of the District Court for the District of Massa- 
chusetts. 



SAMUEL BOWLES AND COMPANY, 
Printers and Binders. 



G& 









AS A MARK OF 

PARENTAL ESTEEM 

FOR HER ATTAINMENTS, 

I DEDICATE 

THESE FEW PAGES TO 

MY DAUGHTER, 

MY COMPANION AND ASSISTANT 
IN THOUGHT AND STUDY, 

AMID THE 

CARES AND PERPLEXITIES 

OF A 
DISTRACTING BUSINESS. 



PREFACE. 



The igneous appearance of a large portion of the earth's crust, 
and its spheroidal figure, which would be incident to a plastic body 
of like dimensions and rotating velocity, have led some geologists 
to believe that the earth may have been, at some early day, in a 
molten condition. Some, on account of various phenomena, have 
conjectured that the central portions may now be in a fluid state. 

But for alleged want of proof, the theory of a melted nucleus is 
very generally rejected. Dana says, " it is still an open question, 
whether the internal heat is that of fusion." It is true that the 
igneous appearance of the crust, and the spherical figure of the 
earth, do not prove its original fluidity. For the centrifugal force 
engendered by the axial rotation, and the denudating and trans- 
porting forces of the ocean in a northerly and southerly direction, 
consequent on the unequal temperatures of the water at the poles 
and equator, would long since have given the earth a spheroidal 
figure, had it been originally created a solid sphere. 

Or had the earth in that ancient day of genesis been created 
without fire, this igneous appearance might have been imparted to 
the crust from volcanoes, if it were possible for them to exist, 
without a melted nucleus. 

It was not from the appearance of the earth, but by the applica- 
tion of nature's laws, that I claim to have shown the convertibility 
of Gravity and Heat, and that the central portions of the earth 
I* 



VI PREFACE. 

must be in a molten condition, among other subjects, treated in a 
pamphlet printed in 1864. While listening to a discussion on the 
physical condition of the moon, by the members of the American 
Academy of Science, held in Northampton in the Summer of 1865, 
I learned that they discarded the theory of a melted nucleus, laying 
great stress on Mr. Hopkins' discoveries. Mr. Hopkins might 
have been correct in his conclusions, had the precession of the 
equinoxes been correctly explained. 

I have revised the article on Gravity and Heat, and annexed four 
unpublished sections, which were originally written several years 
before the publication of the pamphlet, in which I have considered 
the fallacy of the hypothesis of the precession of the equinoxes, as 
originally introduced by Sir Isaac Newton, on which Mr. Hopkins' 
calculations were based ; and also pointed out a few of the errors 
of adopted theories, which are more or less connected with the 
above subject. To establish the truth, it seems necessary to point 
out existing errors, while I appreciate most fully, the wonderful 
discoveries that have been made from time to time. If I take two 
cubes of the same matter equal in dimensions and temperature, one 
weighing a pound and the other a pound and a quarter, and reduce 
them from a moderately high temperature to an equally low one, I 
find that the denser cube will liquefy more ice than the rarer, or 
gives off more heat than the lighter, in reducing their temperature 
equally. If the process of heating, the cubes is continued until 
they are fused, it would require more heat to fuse the denser cube. 
As the excess of heat in the denser cube is not indicated by the 
thermometer, I followed the former usage and designated it latent 
heat in the pamphlet, but according to the dynamic view, it is force. 
That is, as the denser cube contains more matter, it requires more 
heat to overcome the attraction of the cohesion of the particles and 
force them asunder. When the heat disappears it becomes force, 
the equivalent of the heat, heat and force being interchangeable, and 
like matter indestructible. It has been known for ages that heat 
was a force, that it expanded matter and produced motion. The 



PREFACE. Vll 

law of the correlation and conservation of heat and force is con- 
sidered to be established, except in the case of gravity. 

When using the word gravitation before one of the most able 
scientists in the country, I have been informed, that "it is not 
known that there is any gravitation, it may be the residuum of 
electricity, or it may be something else." Experiments indicate 
that electricity will not penetrate space void of matter, as the 
planetary regions are. One writer says, "force is matter in mo- 
tion," and another that "the essence of heat is motion," and 
another that " matter is force." 

It is evident that all matter in the universe has a tendency to 
move toward all other matter, whatever may be the proper form of 
expression. When Newton applied the word attraction, it seems 
that his views were sufficiently broad and comprehensive. He says 
in the Principia : " I here use the word attraction in general for any 
endeavor, of what kind soever, made by bodies to approach to each 
other ; whether that endeavor arises from the action of the bodies 
themselves, as tending mutually to or agitating each other by spirits 
emitted ; or whether it arises from the action of the aether or of the 
air, or of any medium whatsoever whether corporeal or incorporeal 
anyhow impelling bodies placed therein towards each other." When 
expressing the tendency of all matter in the universe to move 
towards all other matter, I shall use the familiar and comprehensive 
expression of attraction of gravitation. Its active force I shall 
consider a gravitating motion, and when this motion is resisted that 
heat is the equivalent. 

In proof of the theories advanced, I shall apply some of the 
laws of nature, and make frequent references to the different arti- 
cles, and introduce some very familiar illustrations. In attempting 
to apply the dynamic theory to the resistance of gravity, or in 
other portions of the discussion of these complex and intricate sub- 
jects, in popular form, I may fail to use the best form of expression. 

Discoveries which have emanated from seats high in learning 
and influence have been very tardily recognized. Newton's biogra- 



Vlll PREFACE. 

pher says of him, that although " he survived the publication of his 
great work more than forty years, yet at the time of his death he 
had not above twenty followers out of England." When Kepler 
introduced his immortal work he said, " It may well wait a century 
for a reader, as God has waited six thousand years for an interpreter 
of his works." 

Therefore when I not only introduce new theories, but combat 
the errors of adopted ones, I may expect to wait long for an impar- 
tial reader. 

Springfield, 1867. 



TABLE OF CONTENTS. 



SECTION I. 

Page. 

Conservation of Gravity in a Fluid Nucleus, . . . ii 



SECTION II. 
Gravitation in the Solar System, 48 

SECTION III. 
Theory of the Tides, 62 

SECTION IV. 
Precession— Nutation— and Obliquity of the Ecliptic, 78 

SECTION V. 
Secular Acceleration of the Moon's Mean Motion, 92 

SECTION VI. 
Principles of Planetary Motion and Ethereal Re- 
sistance, 102 



CONSERVATION OF GRAVITY IN A 
FLUID NUCLEUS. 



SECTION I. 

i. The density of molten matter, congealed 
while subjected to pressure, is greater than if it 
were congealed free from pressure. As the force 
of gravitation decreases inversely as the square of 
the distance from the center of the earth, its con- 
densing force is less powerful on the mountain 
heights than at the level of the sea, and less at the 
equator than near either of the poles. It becomes 
evident by all the tests that we can apply, that the 
force of gravitation determines the density of matter. 

2. The expansive force of heat is antagonistic 
to the condensing effect of gravity, as is seen in 
the expansion of matter, when the temperature is 
increased. But the expansion of a fluid mass when 
its temperature is increased, is less, if the pressure 
is first increased. This is seen in many substances 
when the comparatively slight pressure of a portion 
of the atmosphere is removed from them, by plac- 



— 12 — 

ing them under an exhausted receiver. If we apply 
heat to water in this condition, we see how slight 
an incumbrance overcomes, in a measure, its expan- 
sive force, as in this condition, it expands so as to 
form steam, with less heat. The expansive force of 
heat depends 071 the incumbrance of gravity, and the 
elasticity of the matter heated. . 

3. In the Principia Book II., Prop. 20, Newton 
considers that a single particle is pressed towards 
the center of a spherical fluid mass, by the single 
force of its own gravity, and if the second particle 
rests on the former, that the pressure will be 
doubled. The third particle will make the pres- 
sure treble, the fourth particle will make it quadru- 
ple and so on. 

Newton's law as here given respecting the pres- 
sure, like those given in our text books, to explain 
the expansion and contraction when the tempera- 
ture is increased or diminished, is only applicable 
to matter in certain positions. If the outer surface 
of the first particle coincides with the general level 
of the earth, (which is represented by the surface of 
the ocean about 45 ° north or south of the equator,) 
when we place the second particle upon it, in this 
position, with its magnitude projecting above the 
general level, the pressure would be doubled, but 
as gravitation varies with the altitude, the pressure 
would not be trebled if we apply the third particle, 
and so on. The expansion and contraction conse- 
quent on a variation of temperature, contrary to 
the laws given in the tables of our text-books, also 
vary with the pressure. The exceptions to these 



— 13 — 

laws may not be perceptible in very limited magni- 
tudes, but their effect on the magnitude of the 
earth becomes very perceptible. Without deter- 
mining the amount of the variation in pressure, 
density, expansion or contraction, when the parti- 
cle is encumbered by the weight of superior super- 
ficies at unequal altitudes, I will say that the density 
of matter in all its forms depends on the force of 
gravitation and the weight of particle on particle. 
The expansive force of heat must be considered in 
this connection. (See 2.) 

4. If we fill a hollow tube a few feet in length 
with molten matter, when in a horizontal position, 
and then increase the pressure on the particle by 
placing it in a perpendicular posture, its contents 
are increased in density, and the same matter fails 
to fill the tube in its new position. If the matter 
contained in the tube was not heated, its density 
would not be sensibly affected by the change of 
position and slight increase of pressure. This ex- 
periment shows that the expansive force of heat is 
more readily overcome when matter is heated, and 
that the density of matter depends in a measure on 
the weight of particle on particle, for by placing 
the tube of molten matter in a perpendicular posi- 
tion, gravitation acts less on the matter, for it is 
removed farther from the center of the earth, but 
the pressure and density are greater. 

5. When the density of matter is equal, the 
conducting power is uniform, but if we pulverize a 
solid body, or in any way increase or diminish the 
density of a body, (1) we increase or reduce its 

2 



— i 4 — 

conducting power. It is evident that the conductivity 
of matter increases with the density. 

6. If we apply condensing force to a mass of 
liquid matter, it equalizes itself through the whole 
mass. If the liquid mass has perceptible depth, (4) 
particle rests on particle. The density of a mass 
in this condition is not uniform ; that of the inferior 
limb exceeds that of the superior. 

7. If we apply heat to homogeneous matter 
having uniform density, (5) the conducting power 
tends to equalize the temperature in the mass; if 
the density of the matter is unequal the denser 
portion receives the larger quantity, as the conduc- 
tivity of the strata tends to convey heat towards 
the denser limb. 

8. If we compress two cubes of air or matter 
into a smaller space than they previously occupied, 
they are henceforth less easily compressed. The 
capacity of matter to sustain a crushing force increases 
with the density. As heat, the equivalent of force, 
is made apparent by resistance, the temperature of 
matter is increased by compression, as all sub- 
stances indicate. 

9. Solid substances are more easily compressed 
when their temperature is elevated. (4) The com- 
pressibility of congealed matter therefore increases 
with the temperature. 

10. Fused iron or granite under ordinary pres- 
sure, contracts one-eighth of an inch per foot in 
congealing. If the pressure is diminished at the 
time of congelation, (1) the density decreases but 
the amount of contraction is increased. If the 



— 15 — 

pressure is augmented, matter contracts less than 
one-eighth of an inch, the expansive force of heat 
having yielded to the pressure before congelation 
took place. The amount of contraction in matter 
conseque?it on refrigeration depends in a measure 071 
its density. 

ii. This indicates that there is a point in the 
earth, where matter ceases to contract by pressure 
or expand by heat. Compression increases the 
density of matter, but as matter cannot be annihi- 
lated by pressure, the distance between the parti- 
cles decreases, until the expansive force of heat is 
overcome, and the particles are forced into contact, 
by the overlying superincumbent mass, causing 
what may be termed a stratum of perfectly con- 
densed matter, at a fixed point in the earth, and as 
heat is the equivalent of the intense force resisted, 
it must be intensely hot. 

12. Many have experimented on the sustaining 
strength of the various rocks of which the crust of 
the earth is composed, but these experiments prob- 
ably have not been sufficiently extended, on matter 
varying in density and temperature like the crust 
of the earth, to determine to what height a column 
of rock varying in density and temperature might 
be erected, before its base would become crushed. 
The height of the column would vary with the alti- 
tude, as the weight of matter increases as we pro- 
ceed towards the poles, and decreases as we ap- 
proach the equator, or ascend a mountain. If the 
shaft congealed at any of those several points, its 
length would be affected, for its density would 



— i6 — 

vary with the locality (i). If the shaft was cast in 
a perpendicular position in the earth, it would in- 
crease in density as we approach the base (3) ; the 
increase in density would add to its sustaining 
strength, (8) but as there is more or less heat in the 
surface stratum, the temperature must be increas- 
ing with the density as we descend (7), and the 
sustaining strength would decrease when the tem- 
perature became greatly elevated (9). 

If the tables on the sustaining strength of rocks, 
are not sufficiently explicit to determine just how 
many miles in height a rock column, having these 
varying qualities, must be to crush its base, they 
are sufficiently so to determine the fact, that with 
the weight of comparatively few miles in height, 
the base of a column, composed of any representa- 
tive rock found in the crust of the earth, would be 
crushed. The height of the column would vary, as 
does the force of gravitation, in different localities 
on the surface of the earth. 

13. P'urther experiments may be necessary to 
determine or approximate the line in the earth, 
where we should find the crushing point, which is 
the fluid line, or the line where the fluid interior of 
the earth and the crust come in contact. As the 
density, conducting power, and temperature in- 
crease as we descend in the earth, and the sustain- 
ing strength decreases with the temperature, this 
line must be comparatively near the surface, as the 
sustaining strength of the perpendicular column 
having these qualities would indicate ; and as has 
been shown matter is increasing in density accord- 



— 17 — 

ing to the pressure, but this increase is not main- 
tained to any very great depth, as if so the earth 
would be vastly heavier than it now is. 

The variation in the length or sustaining strength 
of the shaft, whatever it may be at different points 
on the earth, represents the thickness of the crust in 
these several localities. The diameter of the shaft 
may be unlimited, for adding to its base adds equally 
to the superincumbent weight. 

The diameter of the crown of the column may 
represent the surface of the earth, and the diameter 
of the base, the point where the crust comes in con- 
tact with the melted nucleus ; for when the base of a 
solid shaft is crushed, the resistance to the intense 
force (8) is perfect, and the crushed portion must 
be intensely hot, even to fluidity. If the shaft was 
cast in the earth in a perpendicular position, the 
crushed portions could not escape in a lateral di- 
rection, for matter in that direction would also be 
crushed, and it must be equally hot. (7) If we 
attempt to lengthen the shaft by adding matter to the 
crown, the base will crush. If we remove the super- 
incumbent weight from the crown of the shaft, the 
heat will expand the crushed base of the column, 
and the intense fluid heat the equivalent of the 
crushing force will disappear, and the matter will 
be refrigerated. The length of the column will 
not therefore be increased or diminished, by light- 
ening or overloading the crown of the shaft. 

14. Heat, being the equivalent of the force re- 
sisted, not only tends to concentrate in the earth 
by compression, but also by conduction, for it 



tends towards the denser limb (7), which if undis- 
turbed always underlies a rarer stratum, thus con- 
centrating the heat of the earth. Although heat 
is being constantly conveyed from the more central 
portion of the earth to the surface, by thermal 
springs, volcanoes and similar agencies, and beyond 
the surface by the expansive force of the atmos- 
phere, it is not lost, (66) as it is conducted in an 
opposite direction, that is towards the center of 
the earth, by the increasing density, and therefore 
increasing conductivity of the strata in that di- 
rection. The prevailing direction of the currents 
indicates that they tend to produce an equalization 
of temperature ; they therefore move in a general 
sense in opposition to conduction. 

The tendency of heat to concentrate in the earth, 
may be seen when we place the tube of molten 
matter in a perpendicular position : (4) the matter 
contains the same heat, in its new position and de- 
creased figure ; it contains more heat per cube, and 
not only the increase in density (3) and in heat is 
greatest in the lower extremity of the tube, but the 
conducting power is also greatest in the same di- 
rection. 

15. Again, that we may more fully realize the 
tendency of heat to concentrate in the earth, let us 
examine a stratum in a perpendicular column of 
sand. We find that there is a given amount of 
cohesive force per grain, and a perceptible increase 
in the number of grains per inch as we descend, as 
well as an increased resisting force ; (8) we must 
therefore acknowledge that there is a correspond- 



— 19 — 

ing increase of force, the equivalent of heat. If 
we cast a shaft of iron in a perpendicular position, 
the conditions being such that all portions may be 
refrigerated as nearly as possible at the same in- 
stant, we find that there is an increase in density 
and in crushing force, as we descend the shaft, and 
an increased conducting power and consequent in- 
crease of heat in the same direction. If we con- 
tinue to descend on this shaft through the crust, 
we find the same continual increase in crushing 
force, density, conducting power and heat, as far as 
we can penetrate, and as these properties increase 
in matter according to the pressure, we must cal- 
culate on the same increase in the impenetrable 
depths. 

Could we penetrate these depths, we should find 
a line, where matter nearly ceases to contract by 
congelation, and the temperature is near the melt- 
ing point, and by a further descent, we should ar- 
rive at a point where it ceases to contract by pres- 
sure, to a perfectly condensed and intensely hot 
fluid nucleus, uniform in density and temperature. 
(7) Matter outside of this line is lighter per cube, 
sustains less force, and retains less heat. Matter 
inside of this line is of uniform density and tem- 
perature. 

16. The nucleus must be more dense than the 
crust, for a solid cannot rest on a fluid less dense 
than itself. It would sink as would ice on a lake 
that should be overloaded, and if a crushing force 
was placed on the crust equal to that on the melted 
nucleus, it would be crushed by the superincum- 



— 20 — 

bent weight, and made a fluid by the condensation. 
(8) The crust rests on partially fused matter, and 
that on the melted nucleus, and heat is not con- 
ducted from the nucleus to the surface, as matter 
decreases in density and in conducting power in 
that direction. As the crust has been disturbed, 
the decrease in density is not regular ; but the con- 
ductivity of the strata decreases very regularly, 
owing to the intersection of comparatively rare 
matter, in veins, dikes, and fissures, at the time of 
the various disturbances. 

17. The theory of a melted nucleus seems to 
be discarded by many scientists. The American 
Encyclopedia says, " It is controverted by Sir 
Charles Lyell, M. Poisson, and other eminent au- 
thorities, on these grounds. When substances, as 
metals, are melted, their temperature cannot be 
raised a single degree above the point of fusion, so 
long as a piece of the material remains unmelted. 
The same principle is exemplified in the impossi- 
bility of raising water to a higher temperature than 
32 P., so long as a fragment of ice remains in it." 
These objections to a melted nucleus may at first 
seem unanswerable, but they vanish upon investi- 
gation. When a portion of matter on the surface 
of the earth is melted, it often is rarer than the re- 
maining solid portion, and when brought into con- 
tact, the solid portion must be melted if there is 
sufficient heat, as heat is conducted more readily 
towards the denser limb. Metals that do not ex- 
pand by melting or contract by refrigeration, have 
a uniform density whether melted or solid, and 



owing to the equalizing tendency of heat, become 
equal in temperature when they are brought into 
contact. If the fused portion of any substance 
was denser than the remaining solid portion, the 
latter would take a superior position when they are 
brought into contact ; but the temperatue of each 
will approach as near to that of the other, as does 
the density of inferior and superior strata of di- 
minutive thickness. All must be said to be melted 
or all to be congealed, in a mass of matter of this 
magnitude, for it would be impossible to detect the 
variation of temperature in the opposite extremes 
of a stratum of such diminutive thickness, but a 
descent of from fifty to sixty feet, indicates a varia- 
tion of a degree, if viewed independently of the 
varying surface influences. Water unlike the solids 
is a substance that expands when it congeals : the 
line of demarkation between the solid and fluid is 
very abrupt, although the variation of the ther- 
mometer may not be perceptible. The water is in- 
ferior, denser, and warmer than the particles of ice 
that rest upon it. If we place a second layer of 
ice upon the first, rarer than the former, it would 
contain less cohesive and resisting force the equiv- 
alent of heat, and this might be the case with many 
succeeding layers, and the temperature would be 
decreasing as we proceed up. The melted nucleus 
like the water, is denser and hotter than the crust 
that rests upon it, but as the variation of tempera- 
ture, — unlike the case of the water and ice, — is 
considerable, between what may be termed solid and 
fluid, so the distance in the earth is considerable, 



between perfect fluidity and the solid crust, com- 
prising some miles of thickening matter, until we 
arrive at congealed matter, or a solid crust thirty 
miles more or less in thickness. 

1 8. Mr. Hopkins experimented on different rock, 
and concluded that the density and conducting 
power of the inferior strata, far exceeded that of 
the superior, and on this account, inferred that the 
melted nucleus must be hundreds of miles from 
the surface. The temperature of the surface stratum 
is variable, but inside of that if the density and 
conducting power of the crust was uniform, the 
temperature must be equal. In this case, an infe- 
rior stratum of great depth, must have the same 
temperature as a stratum near the surface. But as 
the density of the stratum increases with the pres- 
sure (i), and the conducting power of a stratum 
increases with the density, the nucleus must be 
intensely hot. 

The more rapidly the conducting power decreases, 
as we ascend from the melted nucleus, the nearer 
the surface should we find the fluid line. (17) Mr. 
Hopkins also made investigations to ascertain how 
far the observed amount of precession, might be 
consistent with the existence of a fluid nucleus, so 
that "in assuming the recognized period of preces- 
sion, the shell in question must in order that it pro- 
mote such a result, be at least one thousand miles 
thick." I shall reply to this fallacy in a succeeding 
section. 

19. As the density of matter depends on the 
force of gravitation, matter must have existed prior 



— 23 — 

to its condensation by gravitation, and as the re- 
sistance increases with the density, (8) the matter 
of which the earth is composed must have been 
made hot by the condensation. The time must 
therefore have existed, when the earth was in a 
molten condition. Since the creation, gravitation 
has been producing its effects on the earth, and has 
by its powerful and all-pervading influence increased 
the density of matter, unequally in different por- 
tions of the earth, by the pressure of particle on 
particle, causing the central portions of the earth 
to be the more dense. Heat being more readily 
conducted by the denser matter, has receded from 
the surface to the denser strata, producing a thick- 
ening of the fluid, and in process of time solid 
matter, until we arrive at a depth at which matter 
ceases to contract by pressure and heat ceases to 
recede. The density and conducting power of the 
strata, are such that if the portion of the earth 
which is now the solid crust was in a fluid state at 
creation, the heat would have receded to its present 
limits. 

20. In descending through the crust, which has 
been more or less disturbed, the increase in density 
and in heat would not be regular, and would vary 
in different localities, at the same depth. A large 
portion of the crust became hardened while sub- 
jected to greater pressure, than it is, in the position 
it now occupies, and dissimilar rock and strata vary 
more or less in their densities and power of com- 
municating heat, when formed under equal pressure. 
These disturbances and variations cause the ther- 



— 2 4 — 

mometer to indicate different degrees of tempera- 
ture, in different localities at the same depth. 

21. Conduction has caused the fluid heat, that at 
creation was distributed through the matter that is 
now the solid crust, to recede to the denser stra- 
tum (7). The refrigeration and contraction of the 
surface stratum took place first, that being the least 
dense, and the inferior strata of the crust being re- 
frigerated subsequently, caused a lateral pressure 
on the surface stratum, equal to the contraction of 
matter in the inferior strata by refrigeration, or the 
extra surface found in the general average of the 
heights and depressions on the surface of the earth. 

22. If we calculate the crust to be thirty or even 
fifty miles in thickness, and to have contracted in 
congealing as much as iron or granite, in the same 
circumstances, which would be one-eighth of an 
inch per foot on the surface of the earth, and none 
at the other extremity, viz., the fluid line, the ex- 
pansive force of heat at that depth having been 
overcome by pressure, (11) the medium contraction 
of the crust might then have been less than one- 
sixteenth of an inch per foot, as some substances 
are known to contract less than one-eighth of an 
inch per foot in congealing. Thus the earth would 
have been but a very few thousand feet larger in 
diameter, when in its fluid state than it now is. A 
crust thirty miles in depth may seem thin and un- 
stable, but ice a foot in thickness will sustain many 
tons, and, a few rods in thickness, would sustain 
our largest structures. 

23. As the refrigeration of the inferior strata ad- 



— 25 — 

vanced, a mechanical advantage was gained by the 
heavier portions of the solid crust over the lighter. 
This, together with the lateral pressure on the sur- 
face stratum, elevated the mountains and depressed 
the valleys. As the force of gravity on elevated 
matter decreases inversely as the square of its dis- 
tance from the center of the earth, the continents 
and mountains as they were uplifted became self- 
sustaining. As their weight decreased by their 
elevation, the sustaining spherical form of the crust 
increased by the same, adding part of the weight 
of the mountains and continents to the valleys or 
more depressed portions, bringing an unequal pres- 
sure on many portions of the crust, causing cur- 
rents and counter-currents on the surface, and great 
changes in the solid strata. 

24. The changes which are now taking place are 
comparatively trifling, and more local, and are pro- 
duced mostly by the aqueous agents, which are 
changing the position of matter and disturbing the 
equilibrium which exists in the crust. But the 
tendencies of nature to level the surface of the 
earth, by means of the aqueous agents and other 
forces, are counterbalanced. The removal of mat- 
ter from one locality on the surface of the earth, 
allows as much matter to expand at the fluid line, 
as is caused to contract in another portion of the 
fluid line, by the addition of matter in some other 
locality on the surface. Any portion of the crust 
becoming overloaded is crushed by the force of 
gravity on the superincumbent mass, (13) and made 
a fluid by the resistance ; while an equal amount of 
3 



— 26 — 

the melted matter rises with those portions which 
are becoming lighter, above the line of uniform 
density. As there is less pressure, the melted mat- 
ter expands, the fluid heat disappears with the in- 
tense force, and in process of time a uniform pres- 
sure, density, and temperature, is restored to every 
portion coming in contact with the fluid stratum. 

25. The crust varies in thickness in different lo- 
calities, as would the length of the column, (13) 
producing this uniformity of pressure. The une- 
qual centrifugal force in different portions of the 
earth, does not effect the density, or the thickness 
of the crust only as it affects gravity. Centrifugal 
force poises the force of gravitation in a greater or 
less degree, according to the latitude. The thick- 
ness of the crust increases as we approach the 
equator, as the force of gravity decreases in that 
locality on account of the spheroidal figure of the 
earth. The crust at the sea-level indicates a me- 
dium thickness, and the more elevated portions 
show an increase in thickness equal to the eleva- 
tion. As the diameter of the column very greatly 
exceeds its length, and its base is at the crushing 
point, it is liable to fracture through the shorter 
axis, and when the matter about the crown of the 
shaft undergoes a change of position, the localities 
on the earth where the crust is the most liable to 
fracture, can be designated. 

If matter is being removed from any locality on 
the surface of the earth, as in the case of the crown 
of the shaft, the melted matter recedes from that 
locality. If matter is added to any district it ap- 



— 27 — 

proaches that district. The approach of the fluid 
nucleus to any point is equivalent to the subsidence 
of that point, and its recession from any point is 
equal to the upheaval of that point, when compared 
with the level of the sea, for while the melted nu- 
cleus conforms to the center of pressure, the sea 
maintains a level to that center. The altitude or 
the number of mountains when taken as a whole, 
is not being reduced by the leveling forces. 

26. When large deposits of matter are being 
made in any locality, that locality is subsiding ; 
while the district from which the matter is being 
removed is rising, bringing a longitudinal strain on 
the latter, and a lateral pressure on the former. The 
resistance of rock strata to a crushing force far ex- 
ceeds its tension strength. Those portions of the 
crust which receive a longitudinal strain are liable 
to fracture, as some point near or at the summit of 
those which are being uplifted ; and those portions 
which are receiving the greatest longitudinal strain, 
and are the most liable to fracture and allow the 
melted nucleus to be forced up to the surface, and 
at times to form volcanoes, are those lying nearly 
equidistant between the points of greatest upheaval 
and depression and are near the level of the sea. 
This is the line upon which faults are formed. 

Some portion of the crust near that line and be- 
low it, is receiving matter and is subsiding ; and 
some locality near that line and above it, is losing 
matter and is being uplifted. 

27. When large deposits of foreign matter are 
being made near the coast, that portion of the con- 



— 28 — 

tinent is subsiding. If the district from which 
matter is removed lies contiguous to any sea or 
ocean, that sea or ocean is retiring. Thus the sea 
is encroaching on the land, and the land on the sea, 
as alternately the solid crust is forming the bed of 
an ocean, the summit of a mountain, or is being 
condensed and made a fluid, whether it be igneous 
or aqueous strata. The melted nucleus expands 
and the fluid heat disappears from it as the force is 
removed, forming by this refrigeration the inferior 
stratum of plutonic rock. 

This rock is being formed at points underlying 
the localities where the crust is being lightened, 
(13) and in the course of ages, is laid bare by the 
leveling forces on the summit of some lofty moun- 
tain, and in its turn furnishes material for aqueous 
strata, as compression brings the particles of mat- 
ter nearer together (1), and under the power of 
cohesion, stratified rocks will continue to be formed 
by condensation consequent on overloading. 

28. The older mountains are not always the 
higher, for the large deposits of foreign matter in a 
given direction from the base, causes them gradually 
to subside. The plutonic rock is therefore found 
in different localities, at all the intermediate levels 
between the ocean and the summit of the lofty and 
more recently formed mountains. From the posi- 
tion of the organic remains found in these stratified 
rocks, it is evident that they have at times formed 
the bed of the ocean, and the glacial furrows indi- 
cate that these stratified rocks, as well as the plu- 
tonic rocks, have been at times above the line of 



— 29 — 

perpetual frost, and ground down and defaced by 
the weight of glaciers. 

It has been shown that the elevated and depressed 
portions of the earth are continually changing posi- 
tions. Mountains with glaciers may have existed 
in every latitude on the surface of the earth. Rocks 
having a strong likeness to each other, that are 
found in different localities, and are said to belong 
to particular epochs, were formed by similar agen- 
cies at vastly different ages of the world, as is also 
the case with glacial furrows. Their similarity in 
appearance and structure is no indication that they 
have the same, or any definite age, although geolo- 
gists have styled some former particular period the 
glacial and drift epoch, and named the rocks chrono- 
logically. The energy and extent of glacial action, 
or that of the drift, are not diminished as time ad- 
vances, and they were never in the aggregate more 
active than at the present day. 

Glaciers are grooving and transporting the mo- 
raines as in former days. Icebergs are smoothing, 
striating, and scattering boulders, gravel, and 
drift, on the floor of the ocean, as they did in past 
ages, when the present continents formed the bed of 
the ocean. As the motion of ocean currents, with 
their fields of floating ice which often touch the bed 
of the ocean, is from the poles towards the equator, 
the striae they are producing, and the boulders and 
drift they are conveying, are strewed in a northerly 
and southerly direction, as we have abundant evi- 
dence over the surface of North America, as well 
as in other portions of the globe. 
3* 



— 30 — 

The uplifting of the crust from the level of the 
ocean to the line of perpetual frost, with the conse- 
quent changes in the currents of the ocean, gives 
to the same locality, in the course of years, a change 
of climate. 

29. Since the earth, as a whole has ceased to con- 
tract, these changes have become less rapid ; but a 
few centuries makes them visible, in many locali- 
ties on the surface of the earth. The subsidence 
may be seen near the points where large quantities 
of foreign matter are being deposited, as at the 
estuaries of some rivers, where trees are found buried 
in a growing posture below the level of the sea, as 
well as at other points where edifices have been 
immersed. 

Promontories and even mountains are being sub- 
merged, and are forming islands in those portions 
of a continent which are subsiding, and other moun- 
tains composed of various strata, are being formed 
on those portions which are losing matter and are 
being uplifted. The uplifting of the land from the 
bed of the ocean, is the most apparent at points 
where extended high lands or mountain ranges 
are on the side of the continent bordering on the 
sea, as may be seen on the western coast of 
South America. In favorable circumstances, these 
changes of level are the most rapid, where the sur- 
face inequalities are the most visible, as is seen in 
the warmer climates (62). When many forces have 
combined to change the level of a particular local- 
ity more rapidly, implements of the aborigines have 
become buried to a considerable depth, causing un- 



— 3i — 

necessary doubt in the minds of some few eminent 
men, regarding the accuracy of the mosaic narra- 
tion of the age of man on the earth. 

30. The effects of this upheaval and depression 
are indelibly stamped in various ways on the solid 
crust, as is seen in the various fractures of cleavage, 
dislocation, &c. Fractures which were produced in 
the surface stratum at the summit of an uplift, or 
near the summit, are usually represented by a rent ; 
those underlying the same locality in the inferior, 
hotter and more plastic strata, by a fold. Before 
the faults were disturbed, they were on a line near 
the level of the ocean. But if erosion and denuda- 
tion were very unequal on opposite sides of the 
continent, they may represent a somewhat higher 
altitude. As volcanoes are formed on those lines 
where the changes of level are the most frequent, 
and where the crust receives the greatest longitud- 
inal strain, they are found more or less in belts or 
bands (26). 

31. It is not my purpose to describe the geo- 
graphical or geological features of the earth, to note 
the variation or increase of heat as we descend 
through the crust, or to point out the localities 
where there have been the most frequent changes, 
or the most violent disturbances. These descrip- 
tions have been given, with more or less minute- 
ness, by many writers on physical geography and 
earthquake phenomena. I propose to confine my- 
self to the origin and cause of these conditions and 
disturbances, and indicate the portion of the crust, 
the conditions of the elements, and the seasons of 



— 32 — 

the year in which they are most likely to occur. 
As the currents of seas and oceans, with their den- 
udating and transporting forces, are subjected to 
more frequent fluctuations than inland streams are, 
islands, peninsulas, and promontories, are more fre- 
quently upheaved and depressed, than is the case 
with the main-land ; as may be seen in the penin- 
sula of Italy. 

It has been suggested by writers on physical 
geography, that those inland tropical seas, which 
are receiving a constant influx of salt water through 
their straits, might be filling up with salt, from the 
almost constant evaporation from their surfaces. 
As previously shown (27), any extended portions of 
land, sea, or ocean, which are receiving large de- 
posits of foreign matter, whether of salt, coral, or 
any other substance, are subsiding. There may be 
exceptions to this however. A point may be up- 
lifted, when receiving slight deposits of foreign 
matter, if it is located nearly equidistant between 
two points, each of which is receiving an excess of 
matter, and is subsiding. The uplift would be pro- 
duced by the solidity of the crust, before it is suffi- 
ciently overloaded to cause subsidence, as some 
coral islands in the central portion of the Pacific 
ocean may indicate. 

Some particular localities are being uplifted when 
receiving deposits, if the district as a whole is losing 
an excess of matter, as is seen in some valleys, and 
in lake and volcanic regions. Lakes thus situated 
are gradually filling up, as is the case with Lake 
Geneva. Other localities are being depressed while 



— 33 — 

being lightened, if the surrounding district is re- 
ceiving an excess of matter, as some islands, penin- 
sulas, capes and promontories, indicate. 

32. The subsidence of the heavier portions of 
the crust, and the rising of the lighter portions, is 
in accordance with the effect produced on an arch, 
the equilibrium of which is disturbed by lightening 
or overloading any portion of its span. The heavier 
portion subsides, causing the lighter to rise. 

It is evident that the uplifted portions of the 
crust would be sustained in their elevated positions, 
as they lose a portion of their weight in being ele- 
vated, and as a part of their weight is added to the 
more depressed portions of the crust, in conse- 
quence of that elevation. That portions of the 
crust are being uplifted, and that a part of their 
weight rests on the valleys and more depressed por- 
tions (23), is manifest from the frequent land-slides. 
If it were not so, land-slides would be unknown, 
and perpendicular gravel and earth-banks would 
be a familiar feature in our landscape. 

33. As the crust floats on the melted nucleus (16), 
and the inequalities on the surface poise each other, 
great mountain chains must be balanced by a deep 
sea, or a vast extent of low level plain. Astronomy 
teaches that the diameter of the earth is invariable ; 
the upheavals and depressions must therefore be 
equal. These motions counterbalance the effect of 
the leveling forces, and maintain an equilibrium in 
the inequalities on the surface of the earth. 

The axis of the earth will not sensibly wander 
about or change its position, by the upheaval of 



— 34 — 

new mountains, at different points on the surface 
of the earth, as represented by Newton in the Prin- 
cipia Book I., Prop. 66, for the inequalities poise 
each other. New mountains cannot be uplifted 
without corresponding new depressions. If by any 
gradual denudating and overloading, the width of 
the Atlantic should become sensibly reduced, land 
would be upheaved in the Pacific ocean. 

34. The leveling forces are not producing any 
very perceptible effect on the rocks which project 
above the line of perpetual frost, as is evident from 
their jagged appearance, but at a slightly inferior 
level they are working with great energy, as is seen 
in the heaving of the surface owing to the alternate 
freezing and thawing, and in the action of glaciers 
and torrents ; removing large quantities of matter, 
undermining precipices, forming overhanging cliffs, 
and at times frightful avalanches of earth and rock. 
These particles of rock and earth seek an inferior 
level, their weight is increased, and as they are 
transported to a greater or less distance, they are 
more or less deranging the geographical land-marks. 

35. Although the crust has an arching and self- 
sustaining form, its sustaining strength is limited, 
by the same limited ability existing in the foot of 
the arch, and in the base of the perpendicular col- 
umn (13). The solidity and sustaining strength 
of the crust, are such that it resists this gradually 
leveling process for a while, before yielding to a 
new position. This resistance causes the changes 
of level and the transition in the density of the 
matter to be more or less paroxysmal, rending the 



— 35 — 

solid crust, producing shocks or earthquakes by 
the fracture and concussion, at times forming new 
or reanimating old volcanoes. 

36. The disturbance produced when the crust is 
fractured, varies with the nature of the soil, the 
face of the country, and the height at which the frac- 
tures occur. The motions imparted to the crust on 
the line upon which faults are formed, (26) are very 
complicated and violent, as a portion of the crust 
on that line is being uplifted and a portion depressed. 
When the crust becomes fractured, it frequently 
closes again. We experience, from time to time, 
these complicated motions and disturbances of the 
solid crust, in frightful earthquakes and similar ca- 
tastrophes. When the egress of matter from the 
vents is unobstructed, the disturbing effect of the 
concussion on the surrounding crust is counter- 
acted in a measure. Slight secondary forces are 
sometimes introduced, as the admission of fluids 
into the fractures of the crust, forming steam and 
gases. 

37. Earthquakes more frequently occur when the 
disturbing forces are the most intense and act the 
most in unison, as when the earth is in that part of 
its orbit nearest the sun and moon, or when the sun 
and moon act in conjunction, and a high tide rests 
on the portion about to be depressed, or when there 
is a sudden decrease in the pressure of the atmos- 
phere on the continent, or on a portion of the con- 
tinent and ocean. While the pressure on the land 
would be greatly reduced, equal at times to the re- 
moval of two or three feet of water from the sur- 



- 3 6- 

face, the waters of the surrounding ocean would 
flow in, on account of the greater pressure else- 
where, and keep up the weight on those portions 
being depressed (26). There are also atmospheric 
tides, corresponding with the tides of the ocean. 
When these tides are at their maximum at a given 
point on the ocean, other things being favorable, 
the ebb in the atmospheric tide, causes the barome- 
ter to be at its minimum on the adjoining conti- 
nent. 

As the sun passes the equator twice yearly, and 
the Spring tides are the highest when the sun is in 
that vicinity, earthquakes are most frequent when 
the sun is near the equinox. 

As the land on the surface of the earth is more 
largely situated in the northern hemisphere, and 
has the least amount of ice, snow, and moisture 
resting upon it, when the sun has its most northern 
declination ; and as the disturbances caused by the 
leveling forces have been accumulating during the 
year, and the vertex of the tidal-wave in a measure 
follows the course of the sun in its journey north 
and south, earthquakes frequently occur when the 
sun returns to the Summer solstice. 

38. Irrespective of the conditions which control 
the expansive force of heat (2), a permanent in- 
crease or decrease in gravitation would cause a 
permanent increase or decrease in the density of 
matter (1). When the distance is diminished be- 
tween the sun and any of the planets, the centrip- 
etal and centrifugal forces are increased. As these 
forces act in direct opposition to each other on mat- 



— 37 — 

ter, the tendency is, to increase or reduce the den- 
sity of the bodies, according as these forces are 
increased or reduced. This may be demonstrated 
and fully proved by matter under our immediate 
control. The extreme eccentricity of the orbits of 
comets and their tenuity of substance, causes some 
of their disks to be sensibly reduced as they ap- 
proach the sun, and may cause some of them to be 
self-luminous in that position. As the distances 
between the sun, moon, and earth are continually 
varying, and as the matter of the earth is alter- 
nately approaching, and receding from, the moon, 
by its motion on its axis, the density of the earth 
is very slightly affected by these varying influences. 
These disturbing forces cause continual motion of 
the melted matter in the volcanic vents. 

39. As the artisan is not able to braze up the 
last aperture in the thin shell of a hollow metallic 
globe a few inches in diameter, on account of the con- 
tinually varying pressure of the air resting on the 
inner and outer surfaces, so nature fails to refriger- 
ate the melted matter in the vents, and close up the 
last apertures in the crust, on account of the con- 
stant transposition of the matter in the vents, caused 
by the ever-varying pressure against its inner and 
outer surfaces. For this reason volcanoes will always 
exist on the earth. If the fluid nucleus could be 
in a state of perfect rest, the uniform pressure of 
the solid crust resting upon its surface, would force 
it up through every vent and fissure, to a height 
nearly equal to that of the fluid nucleus before any 
refrigeration and contraction took place. This 
4 



- 3 8- 

phenomenon may be seen in many localities on the 
surface of the earth.* Owing to the continual mo- 
tion of the melted matter, it may be carried still 
further upward by inertia, and form cones above 
that point. As the melted nucleus conforms to the 
center of pressure, and the sea maintains a level 
to that center, (25) the height to which the fluid 
would rise above the surface of the earth, should 
be calculated from the level of the sea, volcanoes 
being more likely to overflow at the sea-level, and 
less likely on the higher points, where the crust is 
thicker. The crust varies in thickness in different 
localities, owing to the variation in the density, in 
the force of gravity, and the unequal sustaining 
strength of the spherical form of the crust, in dif- 
ferent districts and elevations. These inequalities 
and paroxysmal transitions in the density of matter/ 
and the unequal egress of the fluid at the vents, 
giving different degrees of momentum, cause the 
melted matter to overflow, or stand in the vents, at 
different heights as regards the level of the sea. 

40. As unlike matter in dissimilar inferior strata 
is being condensed and made a fluid (13) at differ- 
ent times, by the transposition of matter on the 
surface, various substances may be ejected from the 
same volcanoes or fissures at different times. While 
granite may be the basis of condensed matter, the 
various trap rocks may be the product of different 
fused strata. 

If we would determine the weight of the earth, 

*An illustration of this may be seen, at present, at the quarry of 
Hon. William N. Flynt, at Monson. 



— 39 — 

we should calculate the medium weight of the crust, 
and that of the fluid nucleus. 

41. That the crust is thin, and the interior of the 
earth a fluid, is evident from the limited ability of 
refrigerated matter but a few miles below the sur- 
face, to resist the superincumbent mass of the 
crust, as is indicated in the base of the perpendicu- 
lar column. If we take the intensity of the stratum 
of equitable temperature in connection with the 
centralizing tendency of the crust, (19) it shows 
that the interior must be intensely hot. Although 
heat tends to diffuse a uniform temperature in hori- 
zontal strata of uniform density, (7) when the 
density of any portion of the horizontal stratum 
becomes sufficiently reduced to admit of freezing, 
the power of conduction has become nearly or quite 
obliterated, so that it may remain for ages congealed, 
before being thawed by conduction, as many per- 
manently frozen wells, and similar phenomena in 
various localities indicate. 

42. That we may realize the transitions through 
which the heat and matter of the earth are capable 
of passing, let us take fifty parts of matter, and sub- 
ject forty-nine parts, more or less, in a crucible to 
an intense fluid heat, and then add the remainder. 
It would all become a fluid. If the crust encircling 
the fluid nucleus could be broken up and pushed 
into the melted mass, the heat contained in the 
melted nucleus would restore the earth to its orig- 
inal fluid condition. In process of time, the heat 
would return to its present limits, and the earth 
would assume its present condition. If, after being 



— 40 — 

thus melted, the heat could not recede to its present 
position, it could not now maintain its present lim- 
its. If it was thus melted, the matter composing 
the crust would be expanded, the inequalities of the 
surface would be leveled, and the sphere enlarged, 
but the surface of the earth would not be very 
materially increased, when we consider the undula- 
tions and surface wrinkles of the present formation, 
for the crust originally congealed when the matter 
was thus expanded. 

43. In establishing the law of the conservation 
of gravity and heat, it becomes necessary to show 
that heat disappears from, or increases by the cube 
in, two bodies, as they approach or recede from 
each other, in the same ratio as the force of gravity 
increases or decreases in those bodies. Gravity is 
a constant force, and heat its equivalent when 
resisted. When two bodies are attracted towards 
each other, the equivalent of the force of gravity 
is found in their accelerated motion. When that 
motion is resisted by any force, matter is condensed, 
and heat, the equivalent of the condensing force, is 
made visible. 

44. If we should remove a particle .of matter from 
any point on the surface of the earth, a portion 
of the fluid nucleus underlying that point would 
expand, and heat would disappear with the force. 
The solidity of the crust would resist a transition, 
under a particular point, causing the expansion at 
the interior to extend over a larger surface, but the 
melted nucleus would be diminished by the removal. 
If the matter thus removed was elevated to the 



— 41 — 

upper atmosphere, (as might be represented by 
attaching a body to a balloon,) the loss of heat in 
the portion of the fluid nucleus underlying the point 
from which the matter was removed, would be the 
same, (13) and heat would have vanished from that 
point, as gravity would by the square of the dis- 
tance ; and the elevated body would rest in an at- 
mosphere less dense than that from which it was 
removed. As the conductivity of a homogeneous, 
uniformly dense stratum, diffuses a uniform temper- 
ature in a horizontal direction, (7) the temperature 
of the elevated body would be reduced to that of 
the medium in which it rests, and the frosts of a 
perpetual Winter might rest upon it. But if the 
body elevated has a fixed form, that has prevented 
it from expanding in an equal ratio with the loss of 
gravity, force, the equivalent of heat, has not been 
vanishing from it, as has gravity by the square of 
the distance. This can be made very apparent, if 
we imagine the body elevated a second time ; this 
time beyond the influence of the earth. In this 
last removal, while gravity has vanished inversely 
as the square of the distance, the stored force in the 
body has not vanished, as the body has not been 
expanding. We therefore find that in elevating the 
body and thereby causing gravity to vanish, we 
have not removed the force of cohesion from the 
particles. 

45. As matter must have existed prior to the 
condensing effect of gravity on the same, giving it 
form (19), gravity must have condensed matter 
before cohesion united the particles. As gravity 

4* 



— 42 — 

produced its effects first, it must vanish first. As 
cohesion originally fixed its firm grasp on the par- 
ticles of solid matter by refrigeration, when the 
matter was under the condensing effect of gravity, 
heat must be restored to the solid matter, to cause 
cohesion to vanish, after the condensing effect of 
gravity shall have been removed. As gravity has 
vanished from the elevated body, if we should 
restore the previously refrigerated heat, and fuse the 
elevated body, cohesive force, the equivalent of 
heat, would vanish as has gravity, and the matter 
would expand in an equal ratio. The more rare the 
same substance, the greater is its capacity for force, 
the equivalent of heat, per pound. 

46. As matter existed prior to its condensation 
by gravity, it might exist if gravitation should be 
removed. Gravity has been constantly producing 
its effects on the earth since the creative act, and 
as we are led to believe by Holy Writ* that the 
force of gravitation has been suspended or removed 
from a limited amount of matter, let us for a moment 
consider the effect, if it should be miraculously 
removed from the matter composing the earth. If 
it should be removed gradually,! the melted nucleus 
would expand, severing the crust into fragments, 
and as the fragmentary crust would maintain the 
greater density that pressure gave it, it would sink, 
and as heat is conducted towards the denser limb, 
it must be melted. 

* Exodus, 14, 22; II. Kings, 6, 6; Matt. 14, 26 — 29; and similar 
passages. 

t If it was removed rapidly, fragments of solid matter correspond- 
ing to meteoric matter, might be hurled into the surrounding space. 



— 43 — 

The prophecy in regard to the final consumma- 
tion of all things would be literally fulfilled. The 
heat refrigerated from the crust, when under the 
condensing effect of gravity, would be restored. 
The elements would "melt with fervent heat and 
be dissolved," and the expansion would cause the 
earth to "pass away with a great noise." Gravity, 
heat, and cohesion would vanish, and matter would 
become rarefied in an equal ratio. While gravita- 
tion has power to condense the rarest nebular mat- 
ter and produce heat, heat has power to expand the 
same matter to its original condition, if ever gravi- 
tation should be removed. 

47. As the projectile forces have not been sus- 
pended, if we should restore gravitation to the 
particles of matter from which it had been removed, 
nature, with her present laws, would restore the 
present density, figure, and physical condition of 
the earth, but not its geographical positions. Mat- 
ter would be condensed, and a melted mass would 
be produced. That portion of matter lying nearest 
the surface, not being perfectly condensed by grav- 
ity, would be refrigerated and form the crust. 

48. As the ruins of some great conflagrations are 
not refrigerated in the course of months, and sev- 
eral years often elapse in the refrigeration of matter 
a few feet in thickness, ejected from a volcano at a 
single eruption ; what ages must have elapsed in 
the refrigeration of the solid crust of the earth : 
epochs during which the temperature has been 
gradually decreasing on the surface. If the crust 
had not been disturbed, all portions would sustain 



— 44 — 

force and retain heat, equal to the density and con- 
ducting power of the stratum in which they were 
formed. As it is, all portions have retained heat 
equal to their primitive density and conductivity, 
and to those of the stratum in which they are 
found (20), and as the interior sustains an intense 
pressure, it is intensely hot, and in the economy of 
nature it must be so, in order to maintain motion 
in the fluids, and vitalize all nature. On account 
of the centralizing tendency of heat, if the nucleus 
was not intensely hot, the surface would be ex- 
tremely cold. 

49. The constant transposition of the fluids tends 
to equalization of heat, as is shown by the direction 
and temperature of the prevailing currents (14). 
The currents in the atmosphere tend to equalize its 
temperature, and its conductivity (7) and capacity 
to sustain force by the cubes, increase with its 
density (8), thereby increasing the refrigerating 
forces. Hence a dense atmosphere, on a still clear 
evening, facilitates the deposit of dew, or the ap- 
pearance of frost. 

50. In consequence of the centrifugal force and 
spheroidal figure of the earth, the tendency origi- 
nally must have been to form the inequalities on 
the surface of the earth, nearly parallel with the 
equator (64). But the unequal temperature and 
equalizing tendencies of the air and water, in dif- 
ferent portions of the earth, cause constant trans- 
position of the fluids at the poles and equator, 
maintaining sea-communication in a transverse di- 
rection, from the vicinity of pole to pole, giving 



— 45 — 

form and outline to the continents, and determining 
mainly the direction of mountain chains. Currents 
moving in a northerly and southerly direction, as the 
Gulf stream, move more or less in curves, owing to 
the rotation of the earth on its axis, and always 
tend to flow in a line determined by a composition 
of these forces, wearing away in a measure all in- 
tervening barriers in the course of time. Complex 
currents often cause a deviation, as in the case of 
the union of the Gulf stream with that from Beh- 
ring's Straits. On account of the centralizing 
tendency of heat, if the internal fires should be- 
come extinct, the pulsations of the globe would 
cease. The sun would continue to give motion to 
the atmosphere, but the earth would be transformed 
into a sterile waste. 

51. The unequal temperature and density of 
water in the earth, causes springs. If we apply 
heat to the lower extremity of a column of water, the 
equalizing tendency is made visible by two currents, 
the warm current ascending, conveying the heat in 
an opposite direction from that in which it is con- 
veyed by conduction, and the cold currents descend- 
ing, showing that the internal heat produces mo- 
tion and causes springs, and that artesian wells 
would overflow at, or above the surface of the earth, 
if it was a perfect sphere, as water stands the high- 
est in the ascending limb. The variation in height 
of the water in two contiguous columns depends 
on their length, and on the unequal temperature, 
or weight per cube, of the water in the respective 
columns. Their temperature may be made such as 



- 4 6- 

to cause a variation in their heights, of a foot in 
every twenty-three feet, or over four feet per hun- 
dred. 

52. Water often descends into the ground warmer 
and less dense than it returns. By descending a few 
feet into the earth, we find ourselves below the in- 
fluence of the impinging of the sunbeams on the 
surface, and arrive at a stratum of invariable tem- 
perature which absorbs this extra heat. As the 
water becomes more dense, it continues to descend, 
and takes the place of that below, which has been 
rarefied by the internal heat, and returns to the 
surface forming a spring. If its transit to the sur- 
face is very direct and quick, it may return hot, as 
we have examples in different localities. 

If the temperature of the descending column, is 
reduced to that of the stratum of invariable tem- 
perature through which it passes, the temperature 
of the ascending column may be reduced nearly as 
low, and the water be returned to the surface, 
cooler and more dense than when it left. Thus 
while the water of a refreshing shower may enter 
the ground warm and insipid, it may be returned 
to the surface a cool and invigorating spring. The 
undulating surface and impervious structure of some 
of the inferior strata, are such that natural drainage, 
(which has been incorrectly considered the sole 
cause of springs, whether from natural or artificial 
apertures,) is an important agent in their produc- 
tion. These two forces may act separately or 
unitedly, in the production of springs. 

As water free to move does not sensibly conduct 



— 47 — 

heat, and is but slightly compressible, its density 
may be increased by pressure, and still indicate a 
very high or very low temperature, if the pressure 
is such that it cannot expand to steam or ice. 

As cold water is heavier than warm, and salt 
water heavier than fresh, when the distribution of 
water at the equator is equal to the evaporation, 
the colder and heavier waters of the polar regions 
may move towards the equator in an undercurrent, 
and when the evaporation is nearly constant, or 
greater than the distribution, the hotter, salter and 
heavier waters may sink to an equal depth, and 
move in an opposite direction. 



GRAVITATION IN THE SOLAR SYSTEM. 



SECTION II. 

53. We have considered very briefly the law of 
density, and indicated a few of its effects on the 
earth. I shall consider that the same laws are ap- 
plicable to the Solar System, as matter throughout 
the universe is equally attracted by gravitation, 
and obeys the same mechanical laws. Let us first 
consider some of its effects on the physical condi- 
tion and peculiar motion of the moon. 

54. In reading a paper before a meeting of the 
Academy of Science, noticed in the introduction, 
Prof. Alexander said, in substance, that the center 
of gravity in the moon does not coincide with the 
center of the figure, and that it is located farther 
from the earth, than the geometrical center of the 
moon. But he gave no reason for the statement. 
He may have based his assertion on the mathemat- 
ical calculations of Prof. Hansen, the German 
astronomer. According to his theory, the moon's 
center is more than thirty-three English miles 
nearer us, than its center of gravity. 



— 49 — 

55- I have not seen his original calculations, but 
from the tenor of the following extract, I think that 
the fallacy of his hypothesis rests in his having 
compared the motion of the moon, to that of a ball 
hurled from a gun through the resisting medium of 
the atmosphere. 

"In discharging a ball from a gun, calculation can 
predict the trajectory it will describe. But if the 
ball is not equally dense on opposite sides, it will 
not pursue the same path it would do if homogene- 
ous. Given the difference of density the curve 
can be laid down, and given the curve, the differ- 
ence of density can be determined/' The condi- 
tions are in no wise similar. The motion of the 
moon in celestial space is free from resistance, and 
depends on the centripetal and centrifugal forces, 
as will be shown in Section VI. 

56. If we drop a guinea and a feather in a vacuum, 
they fall through equal spaces in equal times, but if 
let fall in the atmosphere, they do not reach the 
ground at the same instant. If the feather should 
be attached to the guinea, that portion of the guinea 
the farthest from the feather would arrive first, as 
would the heavier side of a ball, when the inequality 
of the density in the opposite sides is considerable. 
It is admitted that centrifugal force is excited in a 
revolving body, and that it increases with the ve- 
locity when the periodic times are equal. The 
periodic times of the superior and inferior limbs of 
the moon must be equal in their revolution around 
the earth. As the superior limb of the moon is the 
more distant from the earth, it moves in a longer 
5 



— 50 — 

orbit. The velocity and centrifugal force of the 
superior limb therefore exceed that of the inferior 
limb. When centrifugal force is engendered in a 
mass of matter of unequal density, the rarer limb 
must move in the longer orbit where it receives 
the greater centrifugal force. That this is a law, 
and that it is applicable to the moon, can be demon- 
strated by matter and force at our command. 

57. If we elongate a sphere of unequal density, 
so as to form an exaggerated representation of the 
figure and density of the moon, and poise it on the 
center of gravity through the shorter diameter, on 
a pivot that is moving in a circle, the longer and 
rarer limb will move in the longer orbit. I poise it 
on the center of gravity, for a force that moves the 
center is equivalent to moving the whole mass, and 
if all the particles are equally free to rotate, the 
axis invariably conforms to the center of gravity 
through the shorter diameter. If the inequality of 
density in the opposite limbs is extreme, the ex- 
periment must be tried in a vacuum. Again if the 
body is poised on the center of the figure, instead 
of the center of gravity, and if the pivot is caused 
to move with unequal velocity in an ellipse, repre- 
senting the motion and path of the moon, the 
denser limb will not move in the longer orbit, but 
will be subject to more frequent axial rotation, 
caused by the unequal momentum existing in the 
opposite limbs. 

According to the law laid down in Section I. the 
density of the inferior limb of the moon must ex- 
ceed that of the superior limb, as gravitation acts 



— 5i — 

with more force on it ; and the density of those 
portions having the greatest centrifugal force, is 
diminished by their being uplifted to a greater dis- 
tance from the center of the mass (25). The rarer 
matter on the moon, as well as that on the earth, 
moves in the longer orbit where the centrifugal 
force is greatest. According to the law of density, 
the center of gravity in the moon must be nearer the 
earth than is the center of the figure, and accord- 
ing to the laws of motion, it could not move in an 
inverted position as -suggested by Prof. Hansen, 
and again, if the trajectory of the moon depends 
on its unequal density ,-it does not depend on gravi- 
tation. 

58. The distance between the sun and moon, be- 
ing far greater than that between the earth and 
moon, the unequal attraction of the earth on the 
opposite limbs of the moon, greatly exceeds that of 
the sun on its opposite limbs. The preponderance 
of terrestrial gravitation on the denser limb of the 
moon, causes it to be a balanced figure, exposing 
only its loaded or denser limb to the earth. 

The balanced condition of the moon explains the 
singular phenomenon, of the uniform rotation of 
the satellites of the different planets on their axes, 
with each revolution in their orbits, although the 
length of their orbits and times of revolution are 
unequal. Laplace said, "it is well known that the 
satellites present always the same face toward Ju- 
piter, as the moon does toward the earth." Herschel, 
when speaking of the most distant satellite of 
Saturn, says, " it is presumed with much certainty 



— 52 — 

that this satellite revolves on its axis, in the exact 
time of rotation about the primary, as we know to 
be the case with the moon, and as there is con- 
siderable ground for believing to be so with all 
secondaries." 

59. The moon is the more stable in its balanced 
position when it has its mean motion in its orbit, 
and its denser side is turned towards the earth and 
sun, as when the moon is in opposition to the sun. 
The unequal momentum in the superior and infe- 
rior limbs of the moon, caused by their unequal 
orbital motion, when taken in connection with the 
varying angular position of the sun and its unequal 
gravitating influence on the opposite limbs of the 
moon, causes the oscillations called the librations of 
the moon, in longitude and also in latitude, as the 
moon is balanced towards the center of the earth, 
and its path varies from the ecliptic. As the moon's 
orbit maintains an angular position from the eclip- 
tic, and the heavier limb of the moon is turned 
towards the center of the earth, the polar axis of 
the moon is inclined to the ecliptic, thus deter- 
mining the Lunar seasons. 

60. By the application of the laws which have 
been cited in the first section, it becomes evident 
that the magnitude of the melted nucleus of the 
earth would be enlarged, the density and conduc- 
tivity of the crust would be increased, its thickness 
would be reduced, and the surface temperature 
augmented, if gravitation should become more for- 
cible, and vice versa. This law is applicable to all 
of the bodies in the solar system, and shows that 



— 53 — 

the density of the melted nucleus of all the planets 
is the same, and that their surface temperature does 
not depend on their distances from the sun. 

61. It is said that gravity on the surface of the 
moon "is not more than one-sixth of terrestrial 
gravity." If we should transport the column (13) 
to the moon, its weight would be reduced nearly 
five-sixths, its length may therefore be increased in 
an equal ratio, before its base would crush. As the 
force of gravitation determines the density of mat- 
ter, if the shaft was originally congealed in the 
moon, its density must be greatly reduced and its 
length increased, to produce sufficient weight to 
crush its base. The length of this last column 
would indicate the thickness, density, and con- 
ductivity of the crust, and the surface temperature 
of the moon. On account of the feeble force of 
gravity on the surface of the moon, owing to its 
diminutive size when compared with the earth, its 
crust must be very rare and thick, and its density 
and surface temperature much less than that of the 
earth ; for the same reason, its atmosphere must 
be very attenuate. I did not determine fully, (3) 
what effect a variation of pressure would have on 
density, but gravity on the moon is said to be one- 
sixth of that on the earth, and its density (that of 
the earth being I), is 0.5657, and the variation in 
the density of the heavenly bodies being all outside 
of the melted nucleus, the crust of the moon must 
be a few hundred miles in thickness. As the une- 
qual refrigeration and contraction of the interior 
and exterior portion of the crust of the earth caused 
5* 



— 54 — 
the inequalities on its surface, (23) and as rarer 
matter contracts more in congealing (10), the con- 
traction and formation of a rare and thick crust 
must cause great surface inequalities, as the disk 
of the moon indicates. 

62. The crust of the earth is the lightest, as well 
as rarest and thickest at the equator. The greatest 
surface inequalities are therefore found in the 
warmer climates, as is seen in the altitude of table 
lands and mountain ranges. The crust being the 
rarest, lightest, and most elevated where it is. the 
least affected by gravitation, more than one-half of 
the land, and the greater altitudes are located in the 
northern hemisphere. For the inclination of the 
earth on its axis and motion in its orbit, causes the 
south pole to approach nearer to the sun than the 
north pole, subjecting it to more powerful attrac- 
tion, as the inequality in the influence of the sun 
on the opposite limbs of the earth increases, as the 
distance between them decreases. The variation 
in the force of gravitation in the two hemispheres 
is exceedingly slight, and the variation in the alti- 
tudes is also very trifling, when compared with the 
mass of the crust. As the line of the apsides of the 
earth makes an entire revolution in about 115,000 
years, as calculated by some astronomers, and the 
uplifts and depressions on the surface are very 
gradually changing their position, the time will ar- 
rive when the excess of land in the northern hemis- 
phere may be transported to the southern. 

63. The decrease in the density of the planets, 
as the force of gravitation on them decreases, indi- 



— 55 — 

cates a homogeneous substance. Their density and 
physical condition are determined by the force of 
gravitation, but the ratio between their density and 
distances from the sun is not regular, as the force 
of gravitation varies with their mass, figure, the 
distance of the surface from the center owing to the 
unequal surface temperature (2), and the gravitating 
influence of each on the other, (as the influence of 
the moon on the earth,) as well as with their dis- 
tances from the sun. 

If we transport the column which represents the 
thickness of the crust of the earth to the planet 
Jupiter, its weight would be increased two and a 
half times, and if the column was originally con- 
gealed in that planet, its density and conductivity 
would be increased, the mass of the melted nucleus, 
would be large, the crust dense and thin, and the 
surface temperature high. As the expansive force 
of heat is the most apparent when matter is the 
least encumbered by gravitation (2), the high sur- 
face temperature has converted the surface fluids 
into a vapory envelope, which encircles the body of 
the planet, making it very rare when taken as a 
whole. 

Since first writing on this subject, I have learned 
that Laplace arrived at the same conclusion re- 
specting the rarity of the matter near the surface 
of the planet Jupiter, when compared with the 
more central portions. "Taking for data, Jupiter's 
mass, diameter and rate of rotation, he calculated 
the degree of compression at the poles which his 
centrifugal force should produce, supposing his sub- 



- 5 6- 

stance to be homogeneous ; and finding that the 
calculated amount of oblateness was greater than 
the actual amount, inferred that his substance must 
be denser towards the center." A high surface 
temperature greatly inflates the outer envelope, as 
Jupiter and the larger planets indicate. The same 
surface expansion may be perceptible in some of 
the comets as they approach the sun. 

64. The loss of gravity must cause the surface 
of the exterior envelope of vapor to be very rare, 
with a correspondingly reduced temperature, as is 
the case with our upper atmosphere. The reflective 
power of vapor is greatly enhanced in a low tem- 
perature, and far exceeds that of land and water. 
That the outer envelopes of some of the larger 
planets are in this condition, is indicated by their 
great reflective powers, as well as by their variable 
surfaces. 

The rapid motion of these planets on their axes 
causes their equatorial diameters largely to exceed 
their polar diameters. When fluids are very sensi- 
bly elevated by centrifugal force, as is the case in 
the larger planets, they will form more or less in 
ridges, at right angles with the axis of rotation. 
This is very easily demonstrated. Light reflected 
from deep ravines and elevated ridges would cause 
the surface to have the appearance of variegated 
belts, and ridges formed of vapor must undergo 
frequent changes by condensation. The physical 
disturbing forces on these planets must have great 
energy, caused in part by the rapid evaporation and 
condensation, which would give unceasing activity 



— 57 — 

to the leveling forces ; and also by their rapid rota- 
tion on their axes, and the mass and unequal revo- 
lutions of their moons. These, and the nearness 
of the fluid nucleus to their surfaces, would cause 
volcanic action on a very grand and extensive scale. 
The immense volumes of dark and heated vapor 
that ascend at times, would reduce the reflective 
power of the vapor hanging over a very large ex- 
tent of surface. At other times, eruptions would 
cause a vast extent of surface to be covered with 
molten matter. The heat ascending from such ex- 
tensive fields of melted lava would, in a measure, 
disperse, or illuminate the vapor suspended over 
an immense extent of surface. These convulsions 
may cause the more permanent spots on the disk 
of Jupiter ; those which do not disappear with a 
reconstruction of the belts. After spots make their 
first appearance, it has been noticed that their ve- 
locity increases, for awhile, with each successive 
rotation. As the ascending vapor leaves the body 
of the planet, its velocity is much less rapid than 
that of the outer envelope which it is penetrating, 
hence the proper motion of the spots is constantly 
increasing, until they acquire the velocity of the 
more rapidly revolving outer envelope. 

As unlike density and temperature admit of dif- 
ferent chemical combinations, the differing density 
and temperature of the planets may cause their va- 
rious colors. 

65. As the force of gravity on the surface of the 
sun is nearly twenty-eight times that of terrestrial 
gravitation, if the column (13) was transported to 



- 5 8- 

the sun, its length would be reduced to one twenty- 
eighth of its length on the earth. If the shaft was 
formed on the sun, its density would be greatly 
increased, still reducing its length. If the length 
of the shaft in the earth, represented a crust twenty- 
eight miles in medium thickness, the column in the 
sun would represent a medium crust considerably 
less than a mile in thickness. The immense power 
of gravitation in the sun, causes the line of uniform 
density to be located so near the surface, that the 
refrigerating forces are insufficient for congelation, 
except now and then the formation of comparatively 
small spots or thin floating islands, in favorable 
positions. That the fluidity of the surface of the 
sun is dependent on the force of gravitation, is indi- 
cated by the spots on its surface being less frequent, 
when Jupiter and Saturn are at the perihelion, as 
was the case in 1 800, and the most frequent when 
they are the farthest from the sun. In observations 
on the solar spots, W. Schwabe has shown, that the 
maximum and minimum of the period of spots, 
agrees very nearly with the periodic times of the 
larger planets. As gravitation is less powerful on 
the equatorial regions of the earth (25), it is also 
less.powerful on the equator of the sun. The spots 
therefore form at times, and points, the least under 
the condensing effect of the force of solar and 
planetary gravitation, and they soon become lique- 
fied by a relative change of position. The expan- 
sive force caused by their rapid liquefaction may 
carry the highly heated gas beyond a medium height, 
by inertia, and account for the lofty protuberances, 



— 59 — 

which have been seen projecting from the surface 
of the sun. The expansive force of heat, and the 
powerful condensing effect of gravitation on the 
surface of the sun, must cause the exterior envelope 
to be very dense highly heated gas ; as it were a 
very dense blaze. It has been determined by ex- 
periments on the polarization of light, that the sur- 
face of the sun is not incandescent, but is in a 
gaseous condition. As the spots or islands float on 
the melted nucleus, their naturally depressed con- 
dition accounts for the openings, where there is a 
visible island. That the gas overhanging the edge, 
or shore of these islands, is to some extent illumin- 
ated by the melted nucleus, producing the penum- 
bra, is obvious by the disappearance of the penum- 
bra at the point of contact, when any two or more 
contiguous isiands intercept the light. 

The faculae may be caused by the accumulation 
^of the floating specks in clusters, sweeping the sur- 
face owing to their mutual attraction, thereby in- 
creasing the brightness of the surrounding surface, 
just before the visible formation of an island. 
When the island first disappears, its perfect fluidity 
may also cause increased brightness. As intense 
density causes intense temperature, and this causes 
matter to appear radiant, the sun must be lumin- 
ous, and as the temperature of a stratum depends 
on its density, the light of the sun must be as per- 
manent as gravitation. 

66. Those who have advocated the original 
fluidity of the earth, have considered that the sur- 
face heat has disappeared by radiation or otherwise 



— 6o — 

in space, by the cooling process, instead of being 
centralized by conduction. It is true that heat ra- 
diates from the surface of the earth, but we have 
no evidence that heat has passed beyond the bounds 
of the atmosphere. Nature saturates the atmos- 
phere with a watery vapor, one of the most power- 
ful absorbents of radiant heat, seemingly that none 
may escape. If any heat ascends beyond the more 
vapory portion of the atmosphere, it encounters a 
rare atmosphere of low temperature, which expands 
by the faintest application of heat, and the heat is 
converted into force, before it reaches the outer- 
most limits of the atmosphere. When the surface 
of the earth was at a fluid temperature, the radia- 
ting force was vastly increased, but at that primitive 
period, all the water on the earth was held in sus- 
pense, forming a vapory envelope which would pre- 
vent any escape of heat. Neither can any be 
conveyed from the earth by conduction, for there is 
no perceptible matter in celestial space — as is shown 
in Section VI. 

The vivifying effect of the sun is only developed 
into a quickening influence of heat and light, on 
its impinging the atmosphere or body of the planet. 
If the temperature of the earth depended on the 
heat actually radiated from the sun, its temperature 
must be increasing, as, in that case, the opaque sur- 
face of the earth could not radiate heat, as fast as it 
received heat from the glowing surface of the sun. 
Heat, being the equivalent of gravity, is as stable 
as gravitation. The resistance that condensed nebu- 
lous matter primitively offered to gravitation (8,) 



— 6i— • 

caused the solar system originally to be in a molten 
condition, and if the force of gravitation should be 
removed, the matter of which the system is com- 
posed would return to its primeval condition. 



THE THEORY OF THE TIDES. 



SECTION III. 



67. The Physical cause of the tides has been a 
controverted subject, during the various ages of the 
world. The ancients, very naturally, early attribu- 
ted them in some way to the influence of the moon, 
as they maintained nearly the same angular posi- 
tion from that satellite. After the law of gravita- 
tion was finally established by Sir Isaac Newton, 
he assumed in the Principia, Book III., Prop. 36 and 
37, that the gravitating influence of the sun and 
moon on the waters of the ocean, would elongate 
the fluid belt that encircles the earth sufficiently to 
produce the ebb and flow of the tides, but he calcu- 
lated the density of the moon to be more than 
double its true density. Mathematicians of a later 
date have decided, that the " lifting power of the 
moon would not raise the water, or produce a tide 
of more than .07 of an inch, were the ocean 10,000 
fathoms deep, and that the disturbing energy of the 
tangential force at its maximum, is only three- 
fourths of the maximum lifting force." 



-6 3 - 

But in advancing theories of the tides, our text- 
books on Physical Geography and Astronomy, have 
diagrams and. statements, showing that there would 
be a high tide formed under the disturbing body, if 
the earth did not rotate on its axis. Sir John W. 
Herschel says, "were the earth indeed absolutely 
fixed, held in its place by an external force, and the 
water left free to move, no doubt the effect of the 
disturbing power would be to produce a single ac- 
cumulation, vertically under the disturbing body." 

68. That the causes of the tides are not satisfac- 
torily explained, (at least to some minds,) is frankly 
admitted by many that adopt the present popular 
explanations. Herschel says, " many persons find a 
strange difficulty in conceiving the manner in which 
they are produced. That the sun, or moon, should 
by its attraction heap up the waters of the ocean 
under it, seems to them very natural. That it 
should at the same time heap them up on the oppo- 
site sides, seems on the contrary palpably absurd!' 

69. In accounting for the tides by the hypotheses 
advanced in our text-books, there is not that analogy 
between cause and effect that should exist, when 
comparing the effect produced by the moon, with 
those produced by other forces of nature. " A va- 
riation of an inch in the mercurial column of a ba- 
rometer, is equal to 13.4 inches in a column of 
water." A variation then of .07 of an inch in the 
mercurial column should cause the water to flow in 
by the greater pressure elsewhere (37), more than 
thirteen times as high as the direct influence of the 
moon would elevate it (6j). As the mercurial col- 



-6 4 - 

umn varies between two and three inches, it should 
elevate a tide in particular localities, nearly fifty 
times as high as the direct lifting force of the moon. 

If the comparatively feeble tangential force of 
the moon, has any sensible effect in piling up the 
waters of the ocean, what vastly greater effects 
should we expect from the wind, when it sweeps 
over the surface of the ocean towards the coast, at 
the rate of one hundred miles the hour, with suf- 
ficient force to, prostrate the sturdy oak and lay low 
extensive forests. The action of the wind, it is 
true, is confined more particularly to the surface, 
but the rapidity with which it forms and reverses 
currents in the ocean, indicates that it would drive 
in the waters of the ocean, much faster than they 
could possibly return by an under-current, on ac- 
count of the immense amount of friction the re- 
turning inferior current must encounter on its entire 
surface. The lateral force of the wind should over- 
come the resistance, as effectually as the gravitating 
influence of the moon. 

70. The variation in the pressure of the atmos- 
phere over a specified locality, should cause at times, 
an elevation or depression of nearly three feet in 
the altitude of the waters of the ocean. The dis- 
turbing effect of these elements should therefore, 
if the adopted theories were correct, not only have 
their accredited effect on the oscillations of the 
ocean, but when they act in unison in favorable lo- 
calities, they should supersede the effect of the sun 
and moon in causing the ebb and flow of the waters, 
and their results should be as much more marked, 



-6s- 

as their forces are more visible than the influence 
of the sun and moon. 

As the earth is very nearly a sphere, and the in- 
fluence of the moon extends equally in all directions, 
if the tangential force of the moon sensibly elevated 
the waters of the ocean, a high tide would al- 
ways encircle a point on the earth directly under 
the moon. If the direct lifting force of the moon 
sensibly elevated the water of the ocean, a high 
tide should culminate more directly under the dis- 
turbing body than is the case, as gravity is an act- 
ive force, and matter free to move, has the greatest 
velocity at the point where it is the most powerfully 
attracted, — the velocity at once decreasing beyond 
that point as is seen when the earth passes the 
perihelion : — the more friction there is to retard the 
accumulating waters, the more it would favor this 
result. 

71. But the theory which seems to many minds 
"palpably absurd," is that given for the formation of 
a high tide on the side of the earth opposite the 
moon. It is said that the tides are principally 
caused by the unequal attraction of the moon, on the 
earth, and on the waters on its opposite sides, while 
the moon is only about one-eightieth the size of the 
earth, and attracts the waters on the earth nearly 
3600 times less powerfully, than the same amount 
of matter in the earth attracts it, as it is nearly 
240,000 miles distant. The moon, then, with its 
comparatively feeble force of gravitation, is said to 
raise the water of the ocean nearly under it, ten 
feet, more or less, and move the earth bodily five 
6* 



— 66 — 

feet, causing the water to hang back on the opposite 
side five feet, although the moon attracts the water 
on the opposite side of the earth, with nearly as 
much force as it does that on the side towards it, 
for only a small portion of its attractive force is lost 
in passing through the earth. According to this 
hypothesis, the attraction of the moon acting in 
conjunction with terrestrial gravitation, is not pow- 
erful enough to attract the water towards itself five 
feet on the opposite side, while the moon, acting in 
opposition to terrestrial gravitation, attracts it ten 
feet on the side towards itself. At a point on the 
earth near the nadir, where a high tide culminates, 
the water of the ocean is drawn by terrestrial grav- 
itation towards the center of the earth, with a 
velocity sixty times as great, as that of the moon in 
its orbit towards the earth, which is nearly eighty 
times as great, as that of the earth towards the moon. 
What then is to prevent the water at the nadir from 
being attracted towards the earth by gravitation, as 
fast as the earth is falling towards the moon. In 
the adopted hypothesis of the tides at the nadir, it 
would seem that the force of terrestrial gravitation 
is ignored, while according to Newton's Principia, 
"the moon's force to move the sea, is to the force 
of gravity as I to 2871400. It is evident that this 
force is far less than to appear sensibly in statical 
or hydrostatical experiments, or even in those of 
pendulums. It is in the tides only that this force 
shows itself by any sensible effect;" and we must 
take into consideration the fact that he considered 
the density of the moon compared with the density 



-6 7 - 

of the earth as 1 1 to 9, while modern tables give 
the density of the moon 0.5657, that of the earth 
being 1. 

72. In proof that "the waters are raised, by the 
difference of the moon's attraction on the superfi- 
cial waters on both sides, and on the central mass," 
Herschel says : " In the theory of the moon, the 
difference of the sun's attraction on the moon, and 
on the earth, gives rise to a relative tendency in 
the moon to recede from the earth, in conjunction 
and in opposition, and to approach it in quad- 
ratures." The planets are poised between the 
centripetal and centrifugal forces, and any slight 
disturbing force enters into a composition with 
these forces, and soon causes a sensible perturba- 
tion. 

But if the earth and moon when free to move 
were " absolutely fixed," or destitute of orbital mo- 
tion, and their mutual attraction as far exceeded 
the unequal attraction of the sun and moon as does 
terrestrial gravitation, which is holding the waters 
of the ocean in their position on opposite sides of 
the earth, gravitation would not cause them to re- 
cede from each other ; on the contrary they would 
come in contact. 

The unequal attraction of the sun and moon on 
the opposite limbs of the earth, may tend to elon- 
gate the fluid belt encircling the earth, but their 
disturbing influence is so small a fraction (67), 
when compared with the other disturbing forces of 
nature, that they might never have been perceptible 
in the oscillations of the ocean, if other forces had 



— 68 — 

not been introduced, by the rotation of the earth 
on its axis. More especially is this apparent, when 
we consider that the points at which the tides cul- 
minate, change their position on the equator nearly 
1040 miles the hour, and that a vastly superior 
force than that assigned, is necessary to cause the 
ebb and flow of the tides. But if the laws of dynam- 
ics are considered, in connection with the influence 
of the sun and moon, I believe the cause of the tides 
will be more satisfactorily explained. 



FIG.L 



Y" b" 




73. If we place a particle of matter at P Fig. 1, 
and give it an impetus towards y, its path will be 
rectilineal, if there is no disturbing influence to 
cause a deviation. Let M represent the moon, and 
repeat the impulse on the particle P ; it will be de- 



-6 9 - 

fleeted by the composition of these forces, from the 
right line P Y into the diagonal P P 1 of the paral- 
lelogram P G P 1 B. If the influence of the moon 
is suspended, and we suppose E to represent the 
earth, with the pole projected towards the observer, 
and give a third impulse to the particle P, it will be 
deflected to the earth at P 2 . If the earth and moon 
have their respective influences, and we again re- 
peat the impulse on the particle P, it will pass above 
the surface of the earth at P 3 , by a composition of 
these forces. The particle P may represent water 
at the equator on the surface of the earth at P 4 , 
with a projectile force of nearly 1,040 miles the 
hour for twelve hours, between the earth and moon 
to P 5 , by the rotation of the earth on its axis. As 
the magnitude and velocity of the particle from P 
to P 3 , may be the same as that of the water from 
P 4 to P 5 , it would be elevated at P 3 . From P 3 to O, 
the waters of the ocean are retarded in their on- 
ward course, as they have a motion from the moon 
between these two points, owing to the rotation of 
the earth. The uplifting forces therefore combine, 
and form a high tide at P 3 , nearly 45 ° back from a 
direct line joining the centers of the revolving and 
disturbing bodies. 

74. As the quantity of matter in the earth, in 
round numbers is eighty times as great as that of 
the moon, their common center of gravity is eighty 
times nearer the former than the latter, and is 
therefore situated about 3,000 miles from the cen- 
ter of the earth, and is represented at E. The 
earth completes a revolution around the moon on 



— 70 — 

the point E, in the same length of time that is re- 
quired by the moon to complete a revolution around 
the earth. The mean distance between the moon 
and point E is invariable, and the motion of the 
earth around the moon may be said to be hinged 
on that point. Let the line L N divide the earth 
into equal sections. In the revolution of the earth 
on its axis, the section P 2 P 5 O has a motion from 
the moon, the opposite section O l P 4 R having a 
motion towards the moon. 

The distances between the moon and the points 
Z and N, are not affected by the motion of the 
earth around the moon : the limbs Z and N must 
therefore have equal velocities of rotation and 
translation. The axis of rotation is then equidis- 
tant between Z and N, but as the earth is falling 
around the moon on the point E, the center of the 
earth C and the limb R are moving in orbits C O l 
and R P. Hence R has a greater velocity towards 
P 4 than P 2 has towards P 5 . 

75. The point in the earth that has the least 
motion, I shall designate the axis of rotation. That 
point is not located at the true center of the earth, 
but somewhat removed from it as is represented at 
A. As its angular position from a line joining the 
moon, and the center of the earth remains invariably 
the same, the retrograde motion of the moon when 
compared with the rotation of the earth on its axis, 
causes the axis of the earth to be unstable, giving 
an eccentric motion to the earth. The longer limb 
is in the direction of P 4 , the shorter limb towards 
P 5 , and the greater centrifugal force engendered on 



— 7i — 

the long limb of the eccentric, forms a high tide 
at R. The accumulation of the waters at P 3 and 
their retardation from this point to O, causes an ebb 
tide at the latter point, and the increased centrifugal 
force on the long limb of the eccentric, tending to 
raise the waters at R, has the effect to cause an ebb 
tide at O 1 . The tendency of the water to flow on 
from P 3 by inertia, and form a high tide on the 
short limb of the eccentric at P 5 , is counterbalanced 
by the decrease in the centrifugal force, which 
allows an equal flow in a transverse direction 
towards the poles* 

76. If the center of the earth C had as rapid a 
motion of translation in its orbit C O 1 around the 
moon, as R has in its orbit R P, the rotating ve- 
locity of R towards P 4 would be no greater than 
that of P 2 towards P 5 . The chord P 4 P 5 would then 
rotate on a true and fixed center at C, or in this 
condition, as Herschel says, "the rotation must be 
performed round an axis or diameter of the sphere, 
whose poles or extremities, where it meets the sur- 
face, correspond always to the same points on the 
sphere." But this requires that the axis of a re- 
volving body have a fixed position in space, or that 
every portion have an equal motion of translation, 
which does not admit of an orbital motion, but re- 
quires that the revolving body move in a rectilineal 
path. The curvilinear path of the moon, with its 
balanced condition as before described, (58) causes 
the moon to have an axial rotation, giving alternate 
day and night to the inhabitants of the moon. 

77. When all portions of a body continually mov- 



— 72 — 

ing in a given direction, have not equal velocities 
of translation, the resultant is a motion of rotation 
on an axis, as well as in an orbit, as is evident in 
the case of the moon. 

Let I represent the inferior limb of the moon, 
and I I 1 , the orbit in which it moves when passing 
around the earth, S the superior limb, and S S l , 
its orbit. It is evident that the point S passes 
around the point I, with each revolution of the 
moon in its orbit, and as the length of the orbit 
S S 1 is equal to that of I I 1 plus the circumference 
of the moon, it is evident that the magnitude of the 
rotating velocity of S over that of I, is equal to the 
axial rotation of the matter at S around that of I. 

Again, the axis of rotation in a revolving body is 
located at a point having the least centrifugal force, 
which is represented at I in the moon and at A in 
the earth. It is well known that solar and sidereal 
time never agree, and that the variation in a year is 
just equal to one revolution of the earth on its axis. 

As the rotating velocity of the limb S is greater 
than that of I, the centrifugal force engendered on 
the superior or longer limb of the eccentric, must 
exceed that on the inferior limb, for this force in- 
creases with the rotating velocity when the periodic 
times are equal (56). As a portion of the earth is 
falling towards the moon, as well as the moon 
towards the earth, the unequal centrifugal force 
which is proven to exist on opposite limbs of the 
moon, determines the fact of the existence of un- 
equal centrifugal force on the opposite limbs of the 
earth. 



— 73 — 

yS. A condition may be conceived, when a devia- 
tion from a rectilineal path will not disturb the 
axis of rotation, as when a projectile is hurled from 
a rifled gun, or if by chance a planet should move 
pole foremost in its orbit, and if the centrifugal 
force engendered by its axial rotation should be 
sufficient to hold its equator invariably in the same 
plane, as is represented in Fig. 2. Let B represent 

...bYV 



a projectile, as having moved through 90 of an 
arc of a circle to B 1 . The sides of the ball B C 
and B 1 C 1 will have passed through equal spaces in 
equal times, as is represented by the dark and 
dotted lines, as these lines are of equal length and 
come in contact with the ball at the same points. 
Or A may represent a planet as having made an 
entire revolution, in an orbit from ABB 1 and D 
to the point of starting, N and S representing the 
axis of rotation, N the north and S the south pole, 
the pole N moving foremost from A to B 1 , the op- 
posite pole S moving in an opposite direction by D 
to the point of starting. In this case, the axis of 
rotation will not be made unstable by the influence 
of foreign matter, or a deviation from a rectilineal 
7 



— 74 — 

path, as all portions of the moving mass have equal 
velocities of translation and rotation. In this ex- 
ample, the surface of the rotating mass is supposed 
to be uniform, and the density of the opposing limbs 
equal. 

79. When Sir John W. Herschel was introduc- 
ing the hypothesis of the precession of the equi- 
noxes, into his valuable work on astronomy, he 
seemed to fear that the motion of the earth as de- 
scribed by him, might lead some of his readers to 
believe that the axis of the earth was unstable, — 
which is really the case. He says "the reader will 
take care not to confound the variation of the posi- 
tion of the earth's axis in space, with a mere shift- 
ing of the imaginary line about which it revolves 
in its interior. The whole earth participates in the 
motion and goes along with the axis, as if it were 
really a bar of iron driven through it. That such 
is the case is proved by two facts.* Second, that the 
sea maintains its level, which could not be the case if 
the motion of the axis were not accompanied with 
a motion of the whole mass of the earth." But the 
ebb and flow of the tides demonstrates the fact that 
the sea does not maintain its level, and it is partly 
because the axis is not accompanied in its motion 
with the whole mass of the earth, producing the 
tides, on the side of the earth opposite the moon. 

80. When we compare the centrifugal force 
which should be apparent on the long limb of the 
eccentric, with the centrifugal force which perpet- 
ually uplifts and sustains the water on the equator, 

*The first will be noticed in the next section. 



— 75 — 

nearly thirteen miles in height, the tidal wave may 
seem very inferior to that which we might expect. 
The fact is, the unequal attraction of the old hy- 
pothesis might uplift a tidal-wave a fractional part 
of an inch, but it is entirely inadequate to the daily 
observed results. A force vastly superior to that 
assigned, is required to uplift a wave in the ocean 
a few feet, as the point at which the tide culminates, 
changes its position on the equator nearly 1040 
miles the hour. And as we proceed in the investi- 
gation, the impossibility of arriving at definite con- 
clusions regarding the height of a tidal-wave, in 
any particular locality on the surface of the earth, 
by theory alone, becomes evident. Several mathe- 
maticians have bestowed great care and patience, 
on the problem of the flow of water in channels 
with a given depth, width, and head. But with the 
irregular depth, the ever-varying direction of ocean 
currents, and outline of the coast, they would 
naturally differ as to the length of time it would 
take the accumulated waters at the equator to flow 
back towards the poles, and form a perfect sphere, 
if the motion of the earth on its axis could be sus- 
pended with impunity,— although the sea is open 
in this direction from the vicinity of pole to pole. 

Or, how high the water at the equator would be 
elevated with the existing centrifugal force, if the 
equatorial plane changed its position in latitude, as 
many miles the hour, as the culminating point of 
the tides do in longitude on the equator. 

The complexity of the problem becomes still 
more apparent, when we consider- the transverse 



-76- 

position of the continents (50), the ever-varying 
magnitude of the distances between the sun, moon 
and earth, with the frequent change in the direction 
of ocean currents, and in the pressure of the atmos- 
phere. 

Again, the unequal velocity and stability of the 
water to resist the disturbing forces consequent on 
the axial rotation, varies with the latitude, and cur- 
rents moving in a northerly or southerly direction 
in the formation or dispersion of a tidal wave, 
move more or less in curves, owing to the rotation 
of the earth on its axis. Having thus noticed a few of 
the component forces which are manifest in the for- 
mation of a tidal wave, the intricacy of the integral 
problem demonstrates the absolute necessity of 
establishing the tables of the tides, in different lo- 
calities, by patient and persistent observation. 
Without further remarks, I shall assert that the 
forces which have been indicated in this treatise, as 
producing the ebb and flow of the tides, are suffi- 
cient to produce this result. 

The effect of the axial rotation of the earth, 
together with the influence of the moon, is piling 
up the waters of the ocean, forming a high tide 
nearly 45 ° back of the zenith, while the increased 
centrifugal force engendered on the long limb of 
the eccentric, by the instability of the earth on its 
axis, is throwing it up forming a high tide on the 
opposite side. 

The sun and planets also have an influence. The 
influence of the sun on the earth's axis, will be no- 
ticed more fully in the next section. 



— 77 — 

8 1. As the earth has a motion of translation 
around the moon, on their common center of gravity 
represented at E Fig. i, some philosophers have 
attempted to account for a high tide near the nadir, 
by the increased centrifugal force this motion may 
engender. According to this hypothesis, N must 
be situated on the long limb of the eccentric, 
(which is not the case), and centrifugal force being 
a secondary force, must be the most apparent back 
of the point where the velocity is the greatest, as 
is seen in the motion of the earth in its orbit after 
it passes the perihelion, or as is seen in the forma- 
tion of a high tide at R, nearly 45 ° back from the 
longest limb of the eccentric. 

Therefore if this motion engendered a high tide 
at the nadir, it would culminate at O, nearly 45 ° 
back of what would in that case be the longest 
limb of the eccentric, and most rapid motion, in- 
stead of at R nearly 45 ° ahead of the force which 
would, by this hypothesis, be producing it. As the 
mean distances between the moon and the points 
Z C and N are invariable, the earth has no motion 
towards the moon in that direction, and the une- 
qual attraction of the moon on the earth could not 
produce the tides at the nadir. 



PRECESSION— NUTATION— AND OBLIQ- 
UITY OF THE ECLIPTIC. 



SECTION IV. 

82. The motion of precession was known to the 
ancients, and modern works on Astronomy have 
made the subject familiar to every reader. Sir 
Isaac Newton found strong opposers to his newly 
discovered theory of gravitation. To silence them 
and establish fully his theory, he must have felt the 
necessity of accounting for all the observed motions 
of the heavenly bodies. The motion of precession 
therefore called upon him most imperatively for an 
explanation. 

83. He attributed it to the unequal attraction of 
the sun and moon on the equatorial and polar re- 
gions, as there is more matter at the equator than 
at the poles. The Newtonian theory, which has 
been adopted by modern astronomers, has some 
shades of plausibility. When the sun and moon 
are not in an equinox, their angular position to the 
redundant matter on the equator, is such that they 



— 79 — 

may seem to attract it more forcibly than they do 
the polar regions. Let E Fig. 3 represent the north 




£*• 



pole of the earth, S the south pole, S in the small 
circle, the sun, M the moon, and KRD and H Q 
T the redundant matter at the equator. The mat- 
ter at the poles is denser than it is on the equator (1), 
and it can be shown, that the unequal attraction on 
the equatorial and polar regions cannot produce the 
observed motion of the poles. 



— 8o — 

84. If the redundant matter on the equator K R 
D tends in any way to follow the sun and moon, by 
any superior gravitating force inherent in it, over 
that of the matter at the north pole E, the angular 
position of the sun and moon to the redundant mat- 
ter on the equator, is such that the tendency would 
be perpetually to move the pole nearly in the same 
direction, diminishing the obliquity of the ecliptic 
until they would coincide. For the action of the 
sun and moon on the matter K D, would tend to 
draw the point R into the plane of the ecliptic, ele- 
vating the south pole and depressing the northern, 
and when they were south of the equator, as repre- 
sented by M 2 S 4 , the motion of the poles would be 
in the same direction, for the action of the sun and 
moon would tend to draw Q into the plane of the 
ecliptic, still elevating the south pole S and equally 
depressing the northern. When the sun and moon 
are in the equinoxes there is no tendency to motion 
in either direction. 

But that the poles of the earth have not a motion 
in the same direction tending to diminish the ob- 
liquity of the ecliptic, was fully proved by Bradley, 
ten years after Newton's death. He found that 
stars situated near the solstitial colure, that were 
almost opposite in right ascension, appeared at 
times to advance north and south, proving a nuta- 
tion of the earth's axis, as if, (viewed by Newton's 
theory), the moon in certain sections of its orbit 
repulsed rather than attracted the redundant mat- 
ter at the equator. 

85. In continuing the investigation respecting 



the Precession of the Equinoxes, the fallacy of this 
hypothesis is still more apparent. It is said that 
the action of the moon on the accumulated matter 
at the equator, causes the poles of the earth to be 
" describing a circle in the heavens around the pole 
of the ecliptic as a center." 

Let E L represent the ellipse in which the North 
pole is moving, and Q R the equator. When the 
north pole E arrives at L in the ellipse, the equator 
it is said would be inclined from its former position 
Q C R to that designated by the dotted line 
Q A R, causing the sun to cross the equator in 
a new position represented at A on the dotted 
line, instead of at C on the line Q C R, its former 
point of intersection, causing the point where 
the sun crosses the equator to move a few rods 
to the westward at every intersection, produc- 
ing what is known as the Precession of the 
Equinoxes. According to this hypothesis, when 
the pole in its circuit E L arrives at the opposite 
side of the ellipse represented at N 2 , the equator 
must be tipped from its original position equally in 
an opposite direction represented by the dotted 
line Q V R. If in the former case, the variation 
in the inclination of the pole causes the sun to 
cross the equator in a new position, at A, a few 
rods west of the point where it previously inter- 
cepted it at C, in this latter case, it must cause the 
sun to intersect the equator in a new position, at 
V, on the dotted line Q V R, a few rods east of 
its previous point of intersection. In this case, the 
motion of precession must be reversed, while the 



— 82 — 



pole of the earth is passing through a section of 
its elliptic orbit. But observation shows a perpetual 
retrogradation, of 50 1-4" of a degree, more or less, 
per annum. The true cause of the retrogradation 
of the equinoctial points from year to year, with 
the variation of the obliquity of the ecliptic, and 
the nutation of the earth's axis, are the subjects of 
this inquiry. 

86. In explaining the tides (74) it was shown 
Fig. 1, that the limb of the earth towards P 4 , had a 
motion towards the moon, and that P 5 had a motion 
in an opposite direction, P 4 being in the long limb 
of the eccentric, and P 5 in the short limb ; and that 
the axis of the earth was at a point represented by 
A, on a line at right angles from the line L, which 
joins the center of the earth with the moon. 



F/G.4. 




-8 3 - 

87. Let us take a northern position in the heav- 
ens on a line with the center of the earth C, as is 
represented in Fig. 4, the moon M being in con- 
junction with the sun S, and the sun in the vernal 
equinox, and project a perpendicular line L from 
the sun, through the center of the moon and earth. 

The axis of rotation in the earth is represented 
at A in this figure, and holds the same angular posi- 
tion to the center of the earth C and line L, as in 
Fig. 1. If we note the motion of the earth and 
moon as they move on in their yearly course, we 
find that when the earth has completed one revolu- 
tion in its orbit, the moon has made nearly thirteen 
in its orbit, falling a fraction of time back from the 
perpendicular line L to M 1 . Let us now project a 
second perpendicular line L 1 , from the center of 
the earth to the moon M 1 . The axis of the earth 
has fallen back and is at A 1 , maintaining the same 
angular position to the center of the earth and lat- 
ter line L 1 , that it did from the former line L. 

The influence of the moon on the earth, as has 
been shown, (75,) causes its axis of rotation to be 
removed from the geometrical center of the mass, 
giving an eccentric motion to the earth. The retro- 
grade motion of the moon when taken in connec- 
tion with the diurnal rotation of the earth, causes 
the earth's axis to be unstable, as it is continually 
dropping back to meet the moon. The earth arrives 
at its starting-point in the heavens at the end of 
its yearly revolution, but its surface is held back by 
the eccentric motion, caused by the instability of 
its axis. 



-8 4 - 

88. Astronomers have stated that the variation 
of the equinoctial points is not uniform, and that 
the obliquity of the ecliptic is diminishing, without 
clearly denning the cause, or limits of these varia- 
tions. I will attempt to point out the position of 
the heavenly bodies, when the variations are the 
greatest and the least, to verify which would require 
patient observation through a long period of time. 
When the influence of the moon reaches the center 
of the earth from the point M 2 , the axis of the earth 
is at A 2 . The short limb of the eccentric is now 
passing under the sun, and when the influence of 
the moon reaches the earth from the point P, the 
axis is at A 3 , and the long limb of the eccentric is 
then passing under the sun. 

89. When the short limb is approaching the sun, 
the falling back of the surface is decreasing from 
year to year, through a portion of its circuit, and 
when the long limb is approaching the sun, there is 
an opposite result. 

If the moon represented at M\ at the end of the 
year, came up to the point M from which it started 
at the commencement of the year, the axis A 1 would 
come up to the point A from which it started : in 
that case there would be no yearly precession. Or 
in other words, if the moon made any exact num- 
ber of revolutions in its orbit, while the earth was 
making one in its orbit, the point 2 on the surface 
of the earth would have returned to 1, the point of 
starting, for at this point all portions of the earth 
have had equal motions of translation, and even 
rotations. But as the moon fails to come up to its 



-85- 

starting-point at the end of the year, the axis repre- 
sented at A 1 does not come up to the point A, and 
the dotted line 2 fails to come up to the dotted line 
1. The distance at the end of the year between 
these two lines, where they intersect the surface of 
the earth, is the amount of the yearly precession. 
The distance between these lines varies more or 
less from year to year. 

90. Astronomers have asserted that the preces- 
sion of the equinoxes for different equal periods of 
time, is not a constant quantity. This is the case, 
as the surface of an eccentric passes unequal spaces 
in equal times. When the sun and planets act in 
conjunction with the moon, or when the distances 
between them and the earth are diminished, the 
axis of the earth deviates more from the true center 
of the earth, and the eccentricity is increased, and 
vice versa. 

The yearly retrogradation of the equinoctial 
points is maximum, when the influence of the moon 
reaches the earth from the point P, if the planets 
act in conjunction, and are at their least distance 
from the earth, as- the longest limb of the eccentric 
is then passing under the sun. It is minimum, 
when the moon has its greatest distance from the 
earth, and is in opposition to the sun and planets, 
the latter having their least distance from the earth. 
The angles between the axes A A 1 and the sun and 
moon in these positions, are such that the lines 1 
and 2 approach very near to each other. But this 
distance is diminished, when the axis is at A 4 and 
the lines 1 and 2 fall on that side of the center of 



— 86 — 

the earth, as when the moon is in opposition to the 
sun. 

The instability of the earth's axis depends mainly 
on the disturbing influence of the sun and moon, 
for the independent influence of the planets must 
be very slight. 

91. In advancing the theory of the stability of 
the axis, Herschel says, " The whole earth partici- 
pates in the motion, and goes along with the axis 
as if it were really a bar of iron driven through it." 
"That such is the case," he says, "is proved by two 
great facts: 1st, that the latitude of places on the 
earth, or their geographical situations with respect 
to the poles, have undergone no perceptible change 
from the earliest ages." Though the axis is un- 
stable, its variation may not have been detected, 
for if the moon made an exact numbec of revolu- 
tions in its orbit, while the earth made one in its 
orbit, the axis would seem to have undergone no 
change at the end of the year, for while the axis 
had continued to drop back to meet the moon, it 
would have fallen back to its point of starting. 

But as the moon does not come up to its start- 
ing-point at the end of the year, the axis drops 
back to meet it in a very diminutive irregular 
ellipse, nearly the same distance that the equinoc- 
tial points drop back to meet the sun, completing 
a retrograde circuit, with each cycle of the moon. 

When the influence of the sun and moon reaches 
the center of the earth through either of the equi- 
noxes, the poles have an equal motion in space. 

92. Thus far in these investigations, the influence 



-8 7 - 

of the disturbing bodies has been considered as 
reaching the center of the earth, through the plane 
of the equator. The precession of the equinoxes 
would therefore exist, if the sun, moon, and planets 
were perpetually in this plane, whether the earth 
were solid or fluid, or had a thick or thin crust ; 
whether it was spherical or had its present figure. 

If we could view the axis of the earth from the 
equinoctial point I Fig. 4, it would be situated at 
A at the extremity of the dotted line I A, and at 
right angles to it. In this position the poles are 
equidistant from the moon, and have an equal mo- 
tion towards that satellite. When the influence of 
the moon reaches the center of the earth through 
either hemisphere, that hemisphere is partially in 
the short limb of the eccentric, and the opposite 
hemisphere is equally in the long limb.* 

93. The inclination of the earth on its axis and 
motion in its orbit, cause the influence of the sun 
and moon to reach the center of the earth through 
the northern or southern hemisphere, except when 
they are in one of the equinoxes. They are repre- 
sented as being in the summer solstice, and reach- 
ing the center of the earth through the northern 
hemisphere in Fig. 3. (83) Let Q R represent 

* This causes the ebb and flow of the tides on the long limb of 
the eccentric, at the nadir in the opposite hemisphere from the dis- 
turbing body. 

The tidal forces would be rapidly decreasing in the higher lati- 
tudes, in consequence of the less rapid axial velocity, were it not 
that the stability of matter to move in a given plane decreases with 
the velocity, and the points at which the tides culminate change 
their position less rapidly. 



the plane of the equator, and M C the ecliptic. 
The south pole S is partially in the long limb of 
the eccentric, and has a more rapid motion towards 
the moon than the north pole E, which is partially 
in the short limb. If the influence of the sun and 
moon was removed from the earth, its path in the 
heavens would become rectilineal, and its axis of 
rotation would occupy the center of its figure. 
With a given axial velocity, the more rapid the de- 
viation from a right line, the further would the axis 
be removed from the center of the figure. 

94. When the sun is in the summer solstice as 
represented in Fig. 3, the south pole, being par- 
tially in the long limb of the eccentric, has a more 
rapid motion towards the moon than the north pole. 
The deviation of the axis from the center of the 
earth in the southern hemisphere, may be repre- 
sented as moving from S 2 to S 3 , when the moon is 
passing from the vernal equinox to the autumnal, 
while the axis may be represented as deviating from 
N to N 1 in the northern hemisphere. When the 
moon is passing from the autumnal to the vernal 
equinox, the deviation would be from N 3 to N 2 in 
the northern hemisphere, and from S to S l in the 
southern. 

95. If the moon was 90 back from its present 
position, the line of the axis would fall between the 
lines S l S 3 and N l N 3 , and when the moon was at 
the nadir, reckoning from its last position, the axis 
would fall between the lines S S 2 and N N 2 . The 
point where the direct line which joins the moon 
with the center of the earth, intercepts the line 



which represents the axis, may be termed the hinge- 
point. When the influence of the sun and moon 
reaches the center of the earth through either hemis- 
phere, the hinge-point is located in that hemis- 
phere, and when through the plane of the equator, 
the hinge-point exists in that plane. The inclina- 
tion of the earth's axis to the ecliptic, together with 
its orbital motion, causes the hinge-point to move 
north and south, elevating or depressing the poles, 
increasing or diminishing the obliquity of the 
ecliptic. 

96. When the disturbing body crosses the equa- 
tor, the pole that was depressed becomes the ele- 
vated pole, and vice versa, producing what is known 
as the nutation of the earth's axis. This would 
restore the pole to its former position, if the moon 
was the only disturbing body, and if it held the 
same position and distance from the earth at the 
end of the year, that it did at the commencement, 
instead of causing the poles to deviate perpetually 
in the same direction, as they must if the motion 
was produced by the action of gravity on the re- 
dundant matter at the equator, according to New- 
ton's hypothesis. 

The stability of matter on the equator to move 
in a given plane, in consequence of the axial rota- 
tion, combines with the motion of nutation, and the 
resultant of these forces tends to equalize the cir- 
cuit of the poles in space. The moon thus far has 
been considered the only disturbing body. The 
sun and planets have their independent influences, 
and at times they act more or less in unison, caus- 
8* 



— go- 
ing the instability of the earth's axis to vary in the 
opposite hemisphere, and the poles of the earth to 
move in an undulating irregular elliptic circuit in 
the heavens, around the pole of the ecliptic. 

97. The obliquity of the ecliptic is greatest when 
the sun is near an equinox, if the sun, moon, and 
planets act in conjunction, and have their greatest 
northern or southern declination and least distance 
from the earth when they pass the Winter or Sum- 
mer solstice, for in this condition the hinge-point 
approaches the equator with the equinox, from its 
extreme northern or southern limits. The obliquity 
is least when the sun and planets are in opposition 
to the moon, and have their least distance from the 
earth ; the moon having its greatest distance and 
least declination when the sun passes the Summer 
or Winter solstice, for in this condition the hinge- 
point deviates least from the plane of the equator. 

98. The return of the poles of the earth to a 
given point in the heavens, and of the plane of the 
equator to a given position when compared with the 
ecliptic, depends on the return of the sun, moon, 
and planets to a given position in the heavens, 
when compared with the center of the earth. 

The upheaval of a mountain, "any where be- 
tween the pole and the equator," will not " cause 
the poles to wander about" sensibly from their true 
position, as asserted by Newton in the Principia, 
for the inequalities on the surface poise each 
other (33). 

The diurnal instability of the earth's axis, is visi- 
ble in the motion of the tides. The effect it has 



— 9 i — 

on precession and nutation, has long entered into 
the calculations of astronomers, and when we con- 
sider the changes of azimuth noticed in the coast 
survey, and the increasing perfection in the way of 
observation, we may hope that the diurnal instabil- 
ity of the earth's axis will soon be considered, in 
astronomical calculations. 



SECULAR ACCELERATION OF THE 
MOON'S MEAN MOTION. 



SECTION V. 

99. When Dr. Halley, and others, compared the 
records of the ancient Chaldean and Arabian astron- 
omers with more modern lunar tables, they consid- 
ered the fact fully established, that the periodic time 
of the moon's revolution is sensibly shorter in 
modern times. The physical cause of this acceler- 
ation greatly perplexed astronomers, through a por- 
tion of the eighteenth century. 

The French Academy of Sciences at Paris, ever 
zealous to advance the cause of science, offered 
their prize of 1770 to induce a thorough investiga- 
tion, to ascertain if it could be accounted for by the 
theory of gravitation. Euler, one of the first 
mathematicians of the age, received the prize, but 
he was unable to solve the problem. He says, 
" there is not one of the equations about which any 
uncertainty prevails, and now it appears to be es- 
tablished by indisputable evidence, that the secu- 
lar inequality in the moon's mean motion cannot 
be produced by the force of gravitation." 



— 93 — 

Earnestly desiring a solution of this intricate 
problem, the Academy of Science continued to offer 
its stimulating prize. 

Euler extended his researches and confirmed his 
previous declaration, saying at the same time, 
"that no doubt henceforth could exist that the ine- 
quality arose from the resistance of an ethereal 
fluid pervading the celestial regions." The resist- 
ance it was said would "lessen her centrifugal 
force. The earth would consequently draw the 
moon closer to herself, thus diminishing the mag- 
nitude of her orbit and decreasing her periodic 
times." 

Others investigated this interesting and perplex- 
ing subject, and received the prize. But none were 
able to account for the acceleration, by the theory 
of gravitation. 

ioo. While the scientists were thus becoming 
skeptical on the theory of gravitation, Laplace re- 
mained a constant believer in the theory. He may 
therefore have felt that necessity was laid upon him 
to assign the physical cause. Herschel says : "It 
was in this dilemma, that Laplace once more 
stepped in to rescue physical astronomy from its 
reproach." And it seems that Laplace ended the 
controversy, by introducing as the cause the 
hypothesis, "that it depends on the secular varia- 
tions of the eccentricity of the earth's orbit." He 
found that " the action of the planets produced 
nothing of the kind." The disturbance he there- 
fore traced most fully to the sun. 

101. But how can the sun "transmit," or as he 



— 94 — 

says "reflect" back to the moon the action of the 
planets, so as to effect its periodic times, without 
affecting the periodic time of the earth, as the earth 
is a near neighbor of the moon ; the orbits of each 
being concave towards the sun, and the moon's 
orbit when viewed from the sun dwindles nearly to 
a point, as the orbit of the moon is only about one- 
half the diameter of the sun. 

The mean distances of the moon from the earth, 
and the moon and earth from the sun, depend on 
the centrifugal and centripetal forces, as these forces 
poise each other. That these forces are constant 
between the sun, moon, and earth, is proved by the 
permanency of the periodic times of the earth. 

On account of the constant variation in the po- 
sition of the planets, any "transmuted" or "re- 
flected " action from them through the sun, would 
impart irregular motions to the earth. That this is 
not the cause of the acceleration of the moon is 
proved by the fact, that it does not equally affect 
the motion of the earth. If the power to accelerate 
springs from the sun, according to Laplace's theory, 
may it not be proved to be in some way inherent 
in that mass, instead of being " reflected from the 
planets." As the planets are poised between the 
centrifugal and centripetal forces (119), if the* at- 
traction of the earth on the moon was in any way 
decreasing, the length of the moon's orbit must be 
increasing, and its periodic time must be decreas- 
ing, instead of being accelerated. 

As the force of gravitation in the sun, moon and 
earth is stable, the mean distances of the earth and 



— 95 — 

moon from the sun, and the mean velocities in their 
orbits, must be invariably the same. 

102. As the irregular velocity of the earth in its 
orbit, as well as its distance from the sun, depends 
on the centripetal and centrifugal forces, it has its 
mean distance from the sun (95,000,000 of miles 
more or less), at the point in its orbit when it has 
its mean motion. For when the magnitude of the 
distance is greater than the mean distance, the ve- 
locity is less than the mean velocity, and when the 
distance is less, the velocity is greater. The mean 
velocity and distance of the earth from the sun in 
its elliptic orbit, would be its invariable distance and 
velocity, if its orbit should conform to a circle. 

The mean radius-vector of the earth in the elliptic 
orbit, would be the invariable radius of the circle. 
The mean distance of the earth from the sun is 
equal to one-half of the transverse axis of the el- 
lipse. The circumference of the circle must there- 
fore be longer than that of the ellipse ; then if the 
earth's orbit is conforming to a circle, its mean mo- 
tion must be increasing, or the periodic time of the 
earth would be decreasing. 

103. The orbits of some of the comets are such 
elongated ellipses, that, should they conform to a 
circle, their orbital velocity must be very greatly 
increased, or else their periodic times must be 
greatly decreased, as there is no increased force to 
accelerate the velocity. We must consider that 
the periodic times of planets would be decreasing 
if their orbit should conform to a circle. This 
might seem to conflict with Kepler's 3rd law, if 



- 9 6- 

that was not based on the ist, that "the planets 
move in ellipses, &c." If the length of the year 
would be increased if the earth's orbit was a circle, 
it would be increasing in length if it was now con- 
forming to a circle. That a variation in the form 
of the earth's orbit might affect the periodic time 
of the earth, is evident from Kepler's second law, 
for the mean radius-vector is invariable, whether 
the earth is moving in the circle or the ellipse and 
by his law, must describe arrears proportioned to 
the times. 

If the form of the earth's orbit is continually 
vibrating between a circle and an ellipse, as it is 
said to be, and the periodic time of the earth is 
equal in the circle and in the ellipse, the arrears 
described cannot be proportioned to the times, as 
the circumference of the circle is greater than the 
ellipse. The discrepancy of several millions of 
miles, existing between authorities regarding the 
mean distance of the earth from the sun, indicates 
the impracticability of determining by observation 
the exact distance of the planets from the sun, or 
the slight effect the peculiar form of any planet's 
orbit may have on its periodic time. The entire 
correctness of Kepler's laws has many times been 
called in question. Laplace said, " they are very 
nearly observed in the motion of the satellites." 
Herschel says, "we learn to regard the laws of 
Kepler as only first approximations to the much 
more complicated ones which actually prevail." 
Again, if the earth's orbit is gradually conforming 
to a circle, the unequal distance, orbital motion, 



— 97 — 

and unequal apparent diameter of the sun, in the 
aphelion and perihelion passages of the earth, must 
be gradually becoming equal. 

According to this hypothesis, the motion of the 
earth must be such that the sun must be approach- 
ing the center of the orbit, for the unequal attrac- 
tion of the sun on the earth in the different sections 
of its orbit, must cause unequal orbital motion 
which does not admit of a circular orbit. 

104. The orbits of the planets are subject to 
perturbations by the effect of each on the other, but 
this does not warrant the assertion that the eccen- 
tricity of the earth's orbit "is and has been since 
the earliest ages diminishing, and this diminution 
will continue, (there is little reason to doubt), till 
the eccentricity is annihilated altogether, and the 
earth's orbit becomes a perfect circle." Were this 
to prove true, it would annul Kepler's first law, and 
the earth would then have an orbit unlike any of 
the planets, since astronomers have studied the mo- 
tion of the heavenly bodies. " The time required 
for these evolutions," Herschel says : "has not been 
calculated," which is most undoubtedly true. 

If the earth's orbit is gradually conforming to a 
circle, it is increasing in length ; then as the moon's 
orbit encircles the earth its length must also be in- 
creased. If the earth's orbit can undergo this 
change in form, increasing in length without affect- 
ing the periodic time, it is impossible that increas- 
ing the length of the moon's orbit under these 
conditions, can diminish the periodic time of the 
moon. 
9 



105. The secular acceleration of the moon's 
mean motion, has been attributed to "the resist- 
ance of an ethereal fluid, pervading the celestial 
regions." If there was any resistance in ethereal 
space which affected the periodic time of the moon, 
its effect would be manifest on the periodic times 
of the earth, and other planets. But as this has at 
times been strongly asserted, I will notice this 
fallacy more particularly in the next section. Al- 
though there are valid objections to all of the theo- 
ries advanced to explain the secular acceleration of 
the moon's mean motions, the existence of the secu- 
lar inequality has been demonstrated by incontesta- 
ble evidence. The very cause of the acceleration 
of the moon's mean motion, therefore becomes an 
exceedingly interesting question. 

106. Laplace, with others, examined the lunar 
theory, with the most scrupulous attention. He 
decided fully that the action was from the sun. If 
he had considered the disturbing effect of the sun 
on the earth's axis, instead of the " reflected " ac- 
tion of the planets from the sun, he would have 
discovered the physical cause. By the law of gravi- 
tation all matter in the universe attracts all other 
matter, and is itself equally attracted. 

The various positions and unequal attraction of 
the planets on the sun, when acting in conjunction 
with matter outside of the solar system, shows that 
the sun must have more or less motion in space. 

The very slow and unequal rotation of the line 
of the apsides (62), indicates the more or less cur- 
vilinear translating motion, with unequal periodic 



— 99 — 

times, of the central masses, around which the 
heavenly bodies are revolving. This motion is, in 
a measure, analogous to the rotating motion of a 
vibrating pendulum, so beautifully illustrated by 
Foucault a few years since. 

Astronomy gives many indications that the sun 
has a proper motion in space. According to Her- 
schel's calculations, it is moving at the rate of 
422,000 miles per diem. The sun then, as well as 
the moon, does not hold the same position at the 
end of the year, that it occupied at the commence- 
ment. 

107. In explaining the physical cause of the 
tides, and the Precession of the Equinoxes, it was 
shown in Figs. 1 and 3, that the deviation of the 
earth from a right line caused by the gravitating 
force of the sun, moon and planets, caused the axis 
of rotation to be removed from the true center of 
the mass, giving an eccentric motion to the earth. 
The independent disturbing effect of the moon on 
the earth's axis, (as may be seen at M 2 A 2 Fig. 4), 
tends to maintain a limb of the eccentric of uni- 
form length, invariably turned towards itself, and 
causes limbs of variable lengths to be passing un- 
der the 'sun. The disturbing effect of the sun is. 
the same in kind, but less in degree. When the 
sun acts in conjunction with the moon, the length 
of the short limb is diminished, increasing the 
longitude of the moon, and vice versa. 

108. If the sun held a fixed position in the heav- 
ens, this disturbance would be compensated at the 
end of the year, for while the moon would have 



— IOO — 

been apparently accelerated in one section of its 
orbit, it would have been retarded equally in the 
opposite section. In this case, no disturbance of 
the earth's axis caused by the sun, could be detected 
at the end of the year. 

As has been shown in regard to precession (89), 
if the moon held the same fixed position at the end 
of the year that it did at the commencement, there 
would be no yearly precession. But the longitude 
of the sun and stars is increased, by the independ- 
ent disturbing effect of the moon on the earth's 
axis, and the moon is accelerated by the disturbing 
effect of the sun on the same. 

On account of the uncertain data respecting the 
proper motion of the sun in space, and the com- 
plex influences of the planets, it may be impossible 
to determine whether the effect of the sun and 
planets, on the earth's axis, would produce the 
amount of acceleration which observation has estab- 
lished, of about n ;/ in a century. 

109. Herschel says "the earth's orbit will become 
a perfect circle, the tables will be turned, and the 
process of ultimate restoration will commence, after 
which it will again open out into an ellipse, the 
eccentricity will again increase, attain a certain 
moderate amount, and then again decrease." By 
this hypothesis, the acceleration will continue while 
the earth's orbit is conforming to a circle, but when 
the orbit begins to form an ellipse, it will be con- 
verted into a continual retardation. 

Laplace says, "Future ages will develop these 
great inequalities, which are periodical, like the va- 



— 101 — 

nations of the eccentricity of the earth's orbit, 
upon which they depend." 

The moon's mean motion will continue to be ac- 
celerated, as long as the sun does not hold a fixed 
position in the heavens ; and it will never be re- 
tarded at any future day, whatever natural variation 
there may be in the form of the earth's orbit, and 
the longitude of the sun and stars will continue to 
increase, as long as the moon accompanies us, in 
our passage through celestial space. 



PRINCIPLES OF PLANETARY MOTION 
AND ETHEREAL RESISTANCE. 



SECTION VI. 

i io. Sir Isaac Newton decided that any ether, 
however subtle, would retard motion, and since 
Newton's day, any apparent inequality in the mo- 
tions of the planets has, by some, been attributed to 
the resistance of an ethereal fluid in celestial space. 

Hence, some of the believers in the vibratory 
ethereal propagation of light, have affirmed that 
the resistance it offered to planetary motion, dimin- 
ished the magnitude of the moon's orbit, and 
caused the accelerated mean motion of the moon. 
Others have compared the trajectory of the moon, 
to that of a ball, projected from a gun through the 
atmosphere. In the Principia Book III., Prop. 42, 
Newton says, that " bodies may, indeed, persevere 
in their orbits by the mere laws of gravity, yet 
they could by no means have at first derived the 
regular position of the orbits themselves from those 
laws." This theory is universally adopted, I be- 
lieve. Robinson says, "we perceive that the eccen- 
tricity of orbits, and mean distances from the sun, 
depend on the amount, and direction of the origi- 



— 103 — 

nal impulse or velocity, which the planets have in 
some way obtained, and it is not necessary that 
the planets should have any definite impulse, either 
in amount or direction, if the direction is not directly 
to or from the sun." I shall invite your attention 
in this section, to a few brief remarks on the laws of 
planetary motion, and shall demonstrate the fallacy 
of a resisting medium in celestial space, and show 
that the direct force of gravitation to and from the 
sun, may primitively have produced planetary mo- 
tion. 

in. When explaining the system of the world in 
the Principia, Newton prefixed a diagram, showing 
that if a body on a lofty mountain, have an impulse 
in a horizontal direction, sufficiently rapid to poise 
the force of gravitation, and return the body to the 
point from which it was projected, it would con- 
tinue to revolve around the earth in an orbit simi- 
lar to that of the moon. 

Or if a body when "projected in free space," is 
"exposed to the action of a central force, varying 
according to the inverse square of the distance," it 
would revolve in a circular orbit, " which would be 
one of the conic sections." 

That Laplace considered this primitive impulse 
transverse to gravitation necessary, when he intro- 
duced his famous genetic hypothesis of the solar 
system, is evident from his remark. "The inertia 
of matter is most remarkable in the motions of the 
heavenly bodies, which, during a great many ages, 
have not suffered any sensible alteration." He 
considered that the nebulous matter originally ex- 



— 104 — 

isting in space, extending far beyond the orbits of 
Neptune, being condensed into a rotating spheroid, 
threw off rings by centrifugal force, from time to 
time, as the rotation became accelerated by the 
gradual condensation. The rings being sustained 
in their elevated positions, by the centrifugal force 
which uplifted them, were left behind becoming 
ruptured, and contracted upon themselves and 
formed planets. The original rotating velocity of 
the rings, gave the planets their primitive impulse, 
transverse to gravitation. 

If the nebulous matter composing the solar sys- 
tem was condensed into a single rotating spheroid, 
there would be no foreign matter in the solar sys- 
tem, to cause any axial disturbance or resistance. 
If this theory was correct, the axis of the rotating 
uplifted circular rings, would be parallel with the 
axis of the central rotating mass. The axes of the 
planets should therefore be parallel, and perpen- 
dicular to the plane of the ecliptic, but on the con- 
trary, some of them, as is the case with Venus, are 
greatly inclined. As the rings uplifted by centrifu- 
gal force must have been perfectly circular, the 
orbits of the planets would have been circles, in- 
stead of ellipses, as established by Kepler's first 
law. If they were originally hurled from a single 
rotating spheroid into space, their orbits should be 
parallel in a given plane, instead of varying as they 
do, more than 34 , and some of the satellites more 
than 78 . 

One of the important evidences mentioned by 
Laplace in substantiating his genetic theory, was 



— io5 — 

f that the planets rotate in a direction the same as 
that in which they go round the sun, and on axes 
approximately perpendicular to their orbits, which, 
since he wrote, has been contradicted in the case 
of Uranus, and still more recently in the case of 
Neptune." 

112. According to this hypothesis, when the su- 
perior rings were thrown off, they must have been of 
enormous circumference, gradually decreasing to the 
more inferior rings. It seems impossible, that an 
uplifted ring could contain the vast amount of mat- 
ter found in Jupiter and its moons, and the next 
rings be sufficiently slender to form the asteroids, 
and the next ring uplifted contain sufficient matter 
to form our earth and accompanying satellite. 

The asteroids must have been formed of inde- 
pendent rings, as they must have been uplifted in 
perfect circles. If they had been fractured in sub- 
divisions, they must have contracted upon them- 
selves and formed a single mass, as would a ring 
with a single fracture. If the rings which accom- 
pany Saturn in his course through the heavens, 
were uplifted from the body of the planet, they 
must be uniform in density and distance from the 
body of the planet, through their entire circumfer- 
ence. For the matter could not have been uplifted 
if it was not free to move, and centrifugal force 
would not uplift matter in this condition, that was 
not uniform in density. The stability of the rings 
of Saturn in their orbits, indicates that the elements 
do not answer the conditions necessary for the ring 
hypothesis. 



— 106 — 

If the orbits of some of the satellites approach 
so nearly to circles that their motion might be ex- 
plained by the ring hypothesis, their axial rotation 
demonstrates that it is not the case, for it is said 
that the unequal axial rotating velocity of the inner 
and outer portions of the rings, gave the planets 
their axial rotation. If so, a similar motion must 
have been imparted to the satellites, but when we 
consider their unequal masses, and the axial rota- 
tion which must have been produced by the ring 
hypothesis, it does not agree with their actual axial 
rotation, which is caused by their balanced condi- 
tion. (58) Kepler's first law demonstrates that the 
matter of which the planets are formed, could never 
have moved in circular orbits ; and comets traverse 
indifferently almost every point in the heavens. 
The fallacy of the ring hypothesis is evident, when 
we compare the rotating velocity of the equator of 
the central mass, with the orbital velocity of the 
nearer accompanying secondary. For instance, by 
the ring hypothesis, when the ring or planet mer- 
cury was thrown off, the sun must have reached to 
the orbit of mercury, and its equatorial axial veloc- 
ity, must have agreed with the orbital velocity of 
that planet, which is nearly 110,000 miles the hour; 
then, as the sun must have contracted, it is* well 
known that its rotating velocity must have increased, 
and centrifugal force increases with the velocity and 
periodic time, but instead of such increased velocity, 
which would have caused fragments of the sun to fly 
off into space, the equator of the sun has a velocity 
of only about 4,500 miles the hour. 



— 107 — 

An impulse " in the direction of lines parallel to 
the horizon/' as set forth by Newton in his diagram 
on the system of the world, and in our text-books 
generally, would be necessary to project a body 
from the earth, and cause it to "go on revolving 
through the heavens," in an obit like the moon, as 
the body has an equal translating velocity with the 
earth. But an impulse parallel with the surface of 
the sun or primaries, was not necessary in the ge- 
netic elements of the planets. 

113. As the density of matter (3) depends on 
the conditions determined by the force of gravita- 
tion, matter must have existed prior to its conden- 
sation, in a gaseous or nebulous form, and this 
primitive condition coincides, I believe most fully, 
with Moses' account of creation in the book of 
Genesis. From that we learn that the heavens and 
the earth had a "beginning," that the matter of 
which the earth is composed "was without form," 
indicating that it was a very rare fluid, to us a 
"void," and darkness was upon the deep "abyss 
of celestial space, until the Spirit of God moved, 
(by the agency of gravitation) upon the face of the 
waters," or fluid, to condense it, (19) "and there 
was light." (6$) When the surface of the earth be- 
came refrigerated and opaque, "God divided the 
light from the darkness," but the length of time 
intervening is not specified. "And God called the 
light day, and the darkness he called night. And 
the evening and the morning were the first day," 
or period. (48) For Peter says, " But, beloved, be 
not ignorant of this one thing, that one day is with 



— io8 — 

the Lord as a thousand years, and a thousand years 
as one day." 

It was necessary that the fluid, or " waters which 
were under the firmament," should be "divided from 
the waters which were above the firmament," in the 
formation of the solar system from nebulous mat- 
ter. After the waters were thus divided, and the 
planets formed, " God called the firmament," or ce- 
lestial space, "heaven." 

The primitive condensation would cause a high 
surface temperature. (19) The water was held in 
suspense, until the surface refrigeration formed 
mountains and valleys (21), as we are told, "there 
went up a mist from the earth, and watered the 
whole face of the ground." When the surface tem- 
perature became sufficiently reduced to allow the 
suspended fluids to be condensed, "the waters un- 
der the heaven were gathered together unto one 
place, (in the depressed portions of the earth), and 
the dry land appeared." When the overhanging 
mist became condensed, the " lights " were set, or 
became visible, in the " firmament of the heavens, 
to give light upon the earth," "to divide the day 
from the night ; and they were for signs, and for 
seasons, and for days, and years." The 1st verse 
of Genesis, in an introductory way, speaks of the 
creation of the heaven and earth. The 2d, 3d, 4th 
and 5th, speak more particularly of the creation of 
the earth. The 6th, 7th and 8th, pertain to the cre- 
ation of the solar system. The 9th, 10th, nth, 
1 2th and 13th again speak of the earth, the 14th, 
15 th, 1 6th, 17th and 18th, of the earth and the 



— 109 — 

appearance of the solar system, after the surround- 
ing mist or waters had been gathered together into 
one place. The last named verses determine the 
division of time into seasons, and days and years, 
as we have them now, except that the length of 
the day has somewhat decreased, since the fourth 
day or period of creation, by the refrigeration and 
contraction of the earth, which took place in the 
early periods of the earth. 

We are therefore induced, by revelation as well 
as by science, to believe that the matter of which 
the earth and planets are formed, originally per- 
vaded space in homogeneous nebulous form. If 
the density of the solar system is calculated by 
this theory, . a square mile of such matter would 
weigh less th#n a cubic inch of our atmosphere, 
and might well be called a " void." 

114. How improbable that matter having this 
great tenuity, should offer sufficient resistance to 
the falling particles, to cause the mass to rotate 
with a velocity sufficiently rapid, to engender the 
centrifugal force, necessary to uplift rings of suffi- 
cient magnitude to form the planets. 

As gravitation was an active force "in the be- 
ginning," stellar and solar motion was coeval with 
gravitation. Planetary matter which was scattered 
through space, must have formed in independent 
rotating bodies, as the form and orbital velocity of 
the planets indicate ; and when we consider the law 
of gravitation, in connection with the proper mo- 
tion of the solar system in space, it becomes evi- 
dent that the matter of which the planets is com- 



— no — 

posed, could not have formed in a single mass as 
indicated by the ring hypothesis. 

An unequal gravitating impulse of the nebulous 
matter in a curvilinear path, towards some foreign 
point in space, when taken in connection with an 
unequal impulse towards the center of the system, 
would cause continually decreasing circular mo- 
tions, in the solar system. This tendency of all 
matter to rotate in a given direction, consequent 
on the curvilinear motion of the solar system, is in- 
dicated by the tendency of any number of inde- 
pendent pendulums, all tending to rotate in a given 
direction. (106.) 

The secular acceleration of the moon's mean 
motion (108), is a proof of the solar motion in 
space. 

115. Let a line be projected through the center 
of the solar sytem, in the direction of the right 
motion of the sun. Let a second and third line 
pass across the diameter of the solar system, from 
opposite directions all in the same plane, passing 
through the center of the system at right angles to 
each other, inclined 45 ° from the first line, with 
their extremities pointing toward fixed stars in the 
distant heavens. 

For illustration, let the moon, earth, and sun, for 
the moment represent particles, or masses of matter, 
freed from gravity and at rest. Let them be located in 
the above order, on the second or third line, their 
distances being greater, than that of the sun, from, 
any foreign matter, toward which the whole system 
is moving ; their present distance from each other 



— Ill — 

being greatly enlarged, and the sun, representing 
the center of the system, poised in its position by 
matter resting on the opposite extremity of the 
same line ; then by the application of the direct 
force of gravitation, the present planetary motion 
would be produced. As the sun is poised in the 
center of the system, its path would be only slightly 
curvilinear in the direction of the foreign matter, 
and the earth and moon would move towards the 
distant mass, less rapidly than the sun, owing to 
their greater distances. The original influence of 
the sun on the earth, and of the sun and earth on 
the moon, would give the earth and moon an im- 
pulse toward the fixed star, on the opposite end of 
the same line. As the earth and moon retain this 
original impulse towards the fixed star, as well as 
all succeeding impulses, their paths are not recti- 
lineal towards the fixed star, nor do they move in 
a right line toward the ever-varying sun. But a 
composition of these diverging impulses, causes 
them to be falling in curvilinear paths ; the moon 
towards the earth, and the earth and moon towards 
the sun, with unequally accelerated velocities, ac- 
cording to the unequal force of the gravitating im- 
pulse, caused by their unequal distances from the 
foreign matter, and from the center of the system, 
until the centrifugal force poises the centripetal. 
Hence, the elementary motions of the planetary 
and stellar systems could have been produced by 
the direct force of gravitation. 

The nebulous matter was primitively distributed 
uniformly through celestial space. When gravita- 



— 112 — 

tion was originally imparted to the matter in the 
solar system, atom attracted atom, and as they 
formed larger particles, and these formed masses, 
they were each propelled towards all other matter. 
As the nebulous matter in the solar system was 
unequally attracted towards a foreign point, and 
towards the center of the system, it must have 
formed in clusters and masses, and moved in curves. 
The particles located on the line which passes 
through the system, and points in the direction of 
the right motion of the sun, must fall into the cen- 
tral mass, as they move nearly in a right line. 
Those lying on a right line projected through the 
system at right angles to the first line, as their mo- 
tion of translation agrees with that of the sun, or 
central mass, would fall into that luminary. Hence 
the magnitude of the sun. 

116. If we again divide the solar system into 
four parts, the first and last mentioned lines mark- 
ing the division, the more central portion of these 
divisions indicates the distance from the sun, where 
the masses next in size would accumulate, answering 
to Jupiter and Saturn. The greater length of the 
orbit, and the space passed over by the superior 
planets, indicates that their mass should exceed 
those of the inferior planets. As their distance 
from the central mass increased, particles would be 
attracted and rotate around the larger mass, agree- 
ing with those of the planets having satellites. 

117. As the matter was originally distributed uni- 
formly through celestial space, the larger masses 
not only received the larger number of atoms, but 



— ii3 — 

they fell a greater distance, with accelerated veloc- 
ity, which would have caused the larger planets to 
have the more rapid axial velocity. But it is not so 
with the sun ; as the point around which it is re- 
volving is far in the distance, its path is nearly in a 
right line. It received large accessions of atoms 
lying in jts nearly rectilineal path. As these fall 
nearly in a right line, the dimensions of the sun 
would be greatly increased, without materially in- 
creasing its axial velocity ; while others falling in 
any direction on a line at right angles to the first 
line, also unite with the sun without tending to in- 
crease its axial rotation. 

1 1 8. When falling bodies of nearly equal dimen- 
sions, as was originally the case, approach each other, 
the centripetal and centrifugal forces are increased ; 
they have a tendency to rotate around each other. 
If they unite, it would be on a line, approaching a 
tangent. 

The equivalent of the resisted force of the falling 
bodies, would be found in their increased axial ro- 
tation, and temperature. As the density of matter 
depends in a measure on its volume, the unequal 
mass and density of the accumulating bodies, gave 
unequal density to the opposite portions of the 
combining mass, as is seen in the motion of the 
satellites, and as may have been the case with the 
rings of Saturn. Aside from the central mass, the 
smaller the body, the less is the original tendency 
to an axial rotation (117); and the nearer the 
satellites are to the primary, the more unequal is 
gravitation on the opposite limbs. (58) Thus the 
10* 



— H4 — 

denser limbs of the satellites, were originally poised 
towards the primaries. Without considering the 
effect the particular form of a planet's orbit may 
have, on the periodic time of the planet, (103) we 
may say that the permanency of these varying 
forces and motions, admits in a general sense of 
the application of Kepler's laws. Thus, as the 
direct force of gravitation undoubtedly was the 
genetic impulse in the formation of the solar sys- 
tem, homogeneous, nebulous matter originally fell 
from a state of rest, and finally formed in masses, 
or in rings, as in the system of Saturn. As they 
originally fell by centripetal force, with accelerated 
velocity, from unequal altitudes towards two com- 
mon centers, until arrested by centrifugal force, 
they caused the orbits of the planets to be more or 
less elliptical, (depending on the original position 
of the matter), and the primary, to be located in 
one of the foci. 

119. The centripetal force and the velocity in- 
crease, as the distance between the bodies is 
diminished, and centrifugal force increases with the 
increased velocity of the bodies, or diminished cir- 
cumference of the orbit. Hence, the nearer the 
body to the primary the more rapid is its orbital ve- 
locity, and vice versa, causing the radius-vector to 
describe arrears proportioned to the times. 

Gravitation, or centripetal force is continually 
tending to bring the secondaries to the primaries, 
and centrifugal force is continually forcing them 
away from those centers. The unequal translating 
velocities of the planets in the different portions of 



their orbits, depend on these forces, instead of any 
inertia that may have been imparted to them at 
creation, (in) This is indicated by the motion of 
comets. As they recede from the sun, their mo- 
tion becomes sluggish and they come nearly to a 
stand-still, their motion of inertia being nearly sus- 
pended at this point, by the gravitating force of 
the sun. In the early genetic day of creation when 
the particles first formed in clusters, they may have 
traveled in all directions in space. But as there is 
a tendency to rotate in a given direction (106), they 
were mainly hurled in that direction as is seen in 
the motion of the planets, and as would be the 
case with any retrograde comet, should it in any 
way get entangled with the planets. The union 
would increase permanently the density and surface 
temperature, and might increase the rotating veloc- 
ity of the planet. 

If the resultant of their translating velocities, 
was less than the velocity of the planet, the planet 
would fall nearer the sun, the Centripetal and cen- 
trifugal forces would be increased, which would in- 
crease the velocity and diminish the periodic times 
of the planet. This may account for the planets 
being generally nearer the sun than are the comets, 
with orbits more nearly circular. 

When the planets first took their form, they may 
have moved more or less in a transverse direction 
from the present plane of their orbits, but as the 
larger and more central masses gravitate more 
powerfully in a transverse direction from the action 
of the centripetal and centrifugal forces, the orbits 



— n6 — 

of the planets and satellites have approximated to a 
given plane, and their axes to parallelism. 

120. The discovery of the three great laws of 
planetary motion by Kepler was sublime, as also 
was Newton's law of gravitation, to account for 
them. Newton conceived that all matter has the 
power to attract all other matter, and that this force 
of attraction decreases inversely as the square of 
the distance from the center of the earth. He 
established this law of gravitation, by comparing 
the magnitude of the deviation of the moon from a 
right line, caused by terrestrial gravitation, with the 
time occupied by a body falling through a given 
space at the surface of the earth. He also consid- 
ered at great length, (Prirrcipia, Book II., Section 6 
and 7), the effect that a resisting medium has on a 
falling body, and in his closing remark he says, 
" the resistance in every fluid, is as the motion ex- 
cited by the projectile in the fluid ; and cannot be 
less in the most subtle ether in proportion to the 
density of that ether, than it is in air, water, and 
quicksilver, in proportion to the densities of those 
fluids." 

It would seem by the number and delicacy of 
Newton's experiments, that he must have arrived 
at correct conclusions, but he did not decide fully, 
whether there be any resistance in space. For 
when bringing forward the theory of the " System 
of the World," he says, "the celestial motions are. 
scarcely retarded, by the little or no resistance of 
the space in which they are performed." It may 
be impossible to decide this question, without ex- 



— in- 
tending the research farther than Newton did, and 
determining what effect resistance has on a falling 
body having an axial rotation ; for if the ethereal 
medium had only the effect to retard the planets, 
their centrifugal force would be diminished, short- 
ening their orbits, possibly without affecting their 
periodic times. Hence if there were any resistance 
we should in this case be unable to detect it. 

121. In the case of the moon, it has been claimed 
that the resistance accelerated its mean motion. 
If Newton was correct in his conclusions, there is 
no subtle ether in the paths of the planets, what- 
ever there may be near the sun, as their motion is 
not resisted, or if any does exist, it does not retard 
the motions of the planets. This is made evident by 
extending the researches of Newton, to bodies 
falling through a resisting medium, while having an 
axial rotation. 

By imparting a rotary motion of a few thousand 
turns a minute, to a solid metallic globe a couple of 
inches in diameter, and allowing it to fall through 
a space of thirty-five feet in the resisting atmos- 
phere, I find it deviates more than three inches 
from a true perpendicular.* 

Although the axial rotation, and deviation of the 
ball from a right line agrees with the axial rotation 
of the earth, and its deviation from a rectilineal 
path, the deviation of the earth is not caused by 
any resistance in space, but by gravity, although if 
the translating and rotating velocities of the earth 

* Balls projected in gunnery from rifles to a superior or inferior 
level must partake of this lateral or drifting motion. 



— 118 — 

could be maintained in a resisting medium, it might 
have its orbital motion without any centripetal force. 

The curvilinear path of the falling ball shows 
that if the translating and rotating velocities were 
perpetuated, it would move in a very small orbit 
without any centripetal force, by the resistance of 
the air acting unequally on the opposite equatorial 
sides of the rotating globe, at right angles with its 
motion of translation. 

122. According to Newton's theory, if there is 
any subtle ether, the falling ball must be resisted, 
and the deviation of the rotating falling ball dem- 
onstrates that if the motion of the planets was re- 
sisted, their masses, variations in axial rotation and 
translating velocities in their orbits, are so unequal, 
that the magnitude of their orbits and periodic 
times must be unequally diminished. 

Their periodic times would not be assignable by 
Kepler's third law, or by Newton's law of gravita- 
tion. The distance between the earth and sun, and 
the periodic time of the earth, would be diminished, 
and the distance between the earth and moon would 
be increased, as would the periodic time of the 
moon, caused by the unequal dimensions and un- 
equal axial rotations of these bodies. On account 
of the decrease in the periodic times of Encle's and 
Fay's comets, Encle assumed that planetary space 
is pervaded by an extremely rare medium. But as 
it is demonstrated that the motion of the planets is 
not resisted, and the orbits of these comets are in- 
terplanetary, the decrease in their periodic times 
cannot be accounted for by that theory. Again 



— ii9 — 

the unequal variation of their periodic times con- 
flicts with the same theory, to account for which it 
has been conjectured, "that the resistance arises 
from collision with innumerable small bodies re- 
volving about the sun." That these bodies exist 
in abundance is evident, but the effect they may 
have on the periodic time of the comets, cannot be 
determined by the falling ball. 

123. When the matter of the solar system was in 
nebulous form, and the force which caused particle 
to attract particle was imparted to it, the planetary 
system, following nature's laws, took its form, fitted 
for life. 

If the force of gravitation should be removed 
from the solar system, many prophecies in Holy 
Writ would be fulfilled. The sun would " become 
black" owing to expansion, but the moon like the 
earth (46) would be melted and " become as blood." 
" And the stars would fall unto the earth, and the 
heavens depart as a scroll when it is rolled togeth- 
er." Rev. 6. 

The expansion of matter in so many conflicting 
directions would tend to restore rest. Again, if we 
look out into the starry heavens, the probability 
that the earth is to be burned up is confirmed. 
Astronomers have computed that more than fifteen 
hundred fixed stars have disappeared within the 
last three centuries. Some of these stars may have 
become opaque and invisible by surface refrigera- 
tion, as is the case with the earth. 

Others have given the most indisputable evidence 
of having been consumed. Their light has broken 



— 120 — 

forth with such splendor, that they could be seen at 
noonday by the naked eye, and at night through a 
canopy of clouds. After the conflagration has been 
visible for a few months, the stars have disappeared. 
May the Creator of the universe, grant that we may 
be prepared for that hour, when our works shall be 
tried by fire. 




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